Bell numbers: Difference between revisions

=={{header|Maxima}}==

It exists in Maxima the belln built-in function.

Below is another way

<syntaxhighlight lang="maxima">

/* Subfactorial numbers */

subfactorial(n):=block(

subf[0]:1,

subf[n]:n*subf[n-1]+(-1)^n,

subf[n])$

/* Bell numbers implementation */

my_bell(n):=if n=0 then 1 else block(

makelist((1/((n-1)!))*subfactorial(j)*binomial(n-1,j)*(n-j)^(n-1),j,0,n-1),

apply("+",%%))$

/* First 50 */

block(

makelist(my_bell(u),u,0,49),

table_form(%%));

</syntaxhighlight>

{{out}}

<pre>

matrix(

[1],

[1],

[2],

[5],

[15],

[52],

[203],

[877],

[4140],

[21147],

[115975],

[678570],

[4213597],

[27644437],

[190899322],

[1382958545],

[10480142147],

[82864869804],

[682076806159],

[5832742205057],

[51724158235372],

[474869816156751],

[4506715738447323],

[44152005855084346],

[445958869294805289],

[4638590332229999353],

[49631246523618756274],

[545717047936059989389],

[6160539404599934652455],

[71339801938860275191172],

[846749014511809332450147],

[10293358946226376485095653],

[128064670049908713818925644],

[1629595892846007606764728147],

[21195039388640360462388656799],

[281600203019560266563340426570],

[3819714729894818339975525681317],

[52868366208550447901945575624941],

[746289892095625330523099540639146],

[10738823330774692832768857986425209],

[157450588391204931289324344702531067],

[2351152507740617628200694077243788988],

[35742549198872617291353508656626642567],

[552950118797165484321714693280737767385],

[8701963427387055089023600531855797148876],

[139258505266263669602347053993654079693415],

[2265418219334494002928484444705392276158355],

[37450059502461511196505342096431510120174682],

[628919796303118415420210454071849537746015761],

[10726137154573358400342215518590002633917247281]

)

</pre>