階乘 (factorial)
階乘是所有小於及等於該數的正整數之積。
正整數 n 的階乘寫作 n!。

用數學表示:



遞歸方式定義:



階乘有無限多個,表列前100個如下︰

0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10! = 3628800
11! = 39916800
12! = 479001600
13! = 6227020800
14! = 87178291200
15! = 1307674368000
16! = 20922789888000
17! = 355687428096000
18! = 6402373705728000
19! = 121645100408832000
20! = 2432902008176640000
21! = 51090942171709440000
22! = 1124000727777607680000
23! = 25852016738884976640000
24! = 620448401733239439360000
25! = 15511210043330985984000000
26! = 403291461126605635584000000
27! = 10888869450418352160768000000
28! = 304888344611713860501504000000
29! = 8841761993739701954543616000000
30! = 265252859812191058636308480000000
31! = 8222838654177922817725562880000000
32! = 263130836933693530167218012160000000
33! = 8683317618811886495518194401280000000
34! = 295232799039604140847618609643520000000
35! = 10333147966386144929666651337523200000000
36! = 371993326789901217467999448150835200000000
37! = 13763753091226345046315979581580902400000000
38! = 523022617466601111760007224100074291200000000
39! = 20397882081197443358640281739902897356800000000
40! = 815915283247897734345611269596115894272000000000
41! = 33452526613163807108170062053440751665152000000000
42! = 1405006117752879898543142606244511569936384000000000
43! = 60415263063373835637355132068513997507264512000000000
44! = 2658271574788448768043625811014615890319638528000000000
45! = 119622220865480194561963161495657715064383733760000000000
46! = 5502622159812088949850305428800254892961651752960000000000
47! = 258623241511168180642964355153611979969197632389120000000000
48! = 12413915592536072670862289047373375038521486354677760000000000
49! = 608281864034267560872252163321295376887552831379210240000000000
50! = 30414093201713378043612608166064768844377641568960512000000000000
51! = 1551118753287382280224243016469303211063259720016986112000000000000
52! = 80658175170943878571660636856403766975289505440883277824000000000000
53! = 4274883284060025564298013753389399649690343788366813724672000000000000
54! = 230843697339241380472092742683027581083278564571807941132288000000000000
55! = 12696403353658275925965100847566516959580321051449436762275840000000000000
56! = 710998587804863451854045647463724949736497978881168458687447040000000000000
57! = 40526919504877216755680601905432322134980384796226602145184481280000000000000
58! = 2350561331282878571829474910515074683828862318181142924420699914240000000000000
59! = 13868311854568983573793901972038940634590287677268743254082129494016000000000000 0
60! = 83209871127413901442763411832233643807541726063612459524492776964096000000000000 00
61! = 50758021387722479880085681217662522722600452898803600309940593948098560000000000 0000
62! = 31469973260387937525653122354950764088012280797258232192163168247821107200000000 000000
63! = 19826083154044400641161467083618981375447736902272686281062795996127297536000000 00000000
64! = 12688693218588416410343338933516148080286551617454519219880189437521470423040000 0000000000
65! = 82476505920824706667231703067854962521862585513454374929221231343889557749760000 00000000000
66! = 54434493907744306400372924024784275264429306438879887453286012686967108114841600 0000000000000
67! = 36471110918188685288249859096605464427167635314049524593701628500267962436943872 000000000000000
68! = 24800355424368305996009904185691715810473992013553676723717107380182214457121832 96000000000000000
69! = 17112245242814131137246833888127283909227054489352036939364804092325727975414064 7424000000000000000
70! = 11978571669969891796072783721689098736458938142546425857555362864628009582789845 319680000000000000000
71! = 85047858856786231752116764423992601028858460812079623588643076338858868037807901 7697280000000000000000
72! = 61234458376886086861524070385274672740778091784697328983823014963978384987221689 274204160000000000000000
73! = 44701154615126843408912571381250511100768007002829050158190800923704221040671833 17016903680000000000000000
74! = 33078854415193864122595302822125378214568325182093497117061192683541123570097156 5459250872320000000000000000
75! = 24809140811395398091946477116594033660926243886570122837795894512655842677572867 409443815424000000000000000000
76! = 18854947016660502549879322608611465582303945353793293356724879829618440434955379 23117729972224000000000000000000
77! = 14518309202828586963407078408630828498374037922420835884678157468806199134915642 0080065207861248000000000000000000
78! = 11324281178206297831457521158732046228731749579488251990048962825668835325234200 766245086213177344000000000000000000
79! = 89461821307829752868514417153983165206980821677957190721386806322783799069350186 0533361810841010176000000000000000000
80! = 71569457046263802294811533723186532165584657342365752577109445058227039255480148 842668944867280814080000000000000000000
81! = 57971260207473679858797342315781091054123572447316259587458650497163901796938920 56256184534249745940480000000000000000000
82! = 47536433370128417484213820698940494664381329406799332861716093407674399473489914 8613007131808479167119360000000000000000000
83! = 39455239697206586511897471180120610571436503407643446275224357528369751562996629 334879591940103770870906880000000000000000000
84! = 33142401345653532669993875791301312880006662862420494871188460323830591312917168 64129885722968716753156177920000000000000000000
85! = 28171041143805502769494794422606115948005663433057420640510191275256002615979593 3451040286452340924018275123200000000000000000000
86! = 24227095383672732381765523203441259715284870552429381750838764496720162249742450 276789464634901319465571660595200000000000000000000
87! = 21077572983795277172136005186993895952297837380613562123229725112146541157275931 74080683423236414793504734471782400000000000000000000
88! = 18548264225739843911479684564554628438022096894939934668442158098688956218402819 9319100141244804501828416633516851200000000000000000000
89! = 16507955160908461081216919262453619309839666236496541854913520707833171034378509 739399912570787600662729080382999756800000000000000000000
90! = 14857159644817614973095227336208257378855699612846887669422168637049853930940658 76545992131370884059645617234469978112000000000000000000000
91! = 13520015276784029625516656875949514214758686647690667779174173459715367077155999 4765685283954750449427751168336768008192000000000000000000000
92! = 12438414054641307255475324325873553077577991715875414356840239582938137710983519 518443046123837041347353107486982656753664000000000000000000000
93! = 11567725070816415747592051623062404362147532295764135351861422812132468071214673 15215203289516844845303838996289387078090752000000000000000000000
94! = 10873661566567430802736528525678660100418680358018287230749737443404519986941792 7630229109214583415458560865651202385340530688000000000000000000000
95! = 10329978488239059262599702099394727095397746340117372869212250571234293987594703 124871765375385424468563282236864226607350415360000000000000000000000
96! = 99167793487094968920957140154189380115818364865126779544437605483849222280909149 9987689476037000748982075094738965754305639874560000000000000000000000
97! = 96192759682482119853328425949563698712343813919172976158104477319333745612481875 498805879175589072651261284189679678167647067832320000000000000000000000
98! = 94268904488832477456261857430572424738096937640789516634942387772947070700232237 98882976159207729119823605850588608460429412647567360000000000000000000000
99! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915 6089414639761565182862536979208272237582511852109168640000000000000000000000
100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915 608941463976156518286253697920827223758251185210916864000000000000000000000000

前100項階乘亦可參考OEIS的A000142

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