Bell numbers: Difference between revisions

<lang zkl>fcn bellTriangleW(start=1,wantRow=False){ // --> iterator

Walker.zero().tweak('wrap(row){

row.insert(0,row[-1]);

foreach i in ([1..row.len()-1]){ row[i]+=row[i-1] }

wantRow and row or row[-1]

}.fp(List(start))).push(start,start);

}</lang>

<lang zkl>println("First fifteen Bell numbers:");

bellTriangleW().walk(15).println();</lang>

First fifteen Bell numbers:

L(1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213597,27644437,190899322)

</pre>

<lang zkl>println("Rows of the Bell Triangle:");

bt:=bellTriangleW(1,True); do(11){ println(bt.next()) }</lang>

{{out}}

<pre>

Rows of the Bell Triangle:

1

1

L(1,2)

L(2,3,5)

L(5,7,10,15)

L(15,20,27,37,52)

L(52,67,87,114,151,203)

L(203,255,322,409,523,674,877)

L(877,1080,1335,1657,2066,2589,3263,4140)

L(4140,5017,6097,7432,9089,11155,13744,17007,21147)

L(21147,25287,30304,36401,43833,52922,64077,77821,94828,115975)

</pre>

{{libheader|GMP}} GNU Multiple Precision Arithmetic Library

<lang zkl>print("The fiftieth Bell number: ");

var [const] BI=Import("zklBigNum"); // libGMP

bellTriangleW(BI(1)).drop(50).value.println();</lang>

{{out}}

<pre>

The fiftieth Bell number: 10726137154573358400342215518590002633917247281