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A204618 a(n) = n^2 * B(n) where B(n) are the Bell numbers, A000110.

%I A204618 #18 Jul 01 2022 12:23:42
%S A204618 0,1,8,45,240,1300,7308,42973,264960,1712907,11597500,82106970,
%T A204618 606757968,4671909853,37416267112,311165672625,2682916389632,
%U A204618 23947947373356,220992885195516,2105619936025577,20689663294148800,209417588925127191,2181250417408504332
%N A204618 a(n) = n^2 * B(n) where B(n) are the Bell numbers, A000110.
%H A204618 Muniru A Asiru, <a href="/A204618/b204618.txt">Table of n, a(n) for n = 0..550</a>
%F A204618 E.g.f.: (x+x^2+x^2 exp(x))exp(exp(x)+x-1) which is x*A'(x) where A(x) is the e.g.f. for A070071.
%t A204618 nn=20;a=Exp[Exp[x]-1];Range[0,nn]!CoefficientList[Series[x D[x D[a,x],x],{x,0,nn}],x]
%t A204618 Table[n^2 BellB[n],{n,0,30}] (* _Harvey P. Dale_, Jul 01 2022 *)
%o A204618 (GAP) List([0..22],n->n^2*Bell(n)); # _Muniru A Asiru_, Apr 20 2019
%o A204618 (Python)
%o A204618 from itertools import count, accumulate, islice
%o A204618 def A204618_gen(): # generator of terms
%o A204618     yield 0
%o A204618     blist, b = (1,), 1
%o A204618     for n in count(1):
%o A204618         blist = list(accumulate(blist, initial=(b:=blist[-1])))
%o A204618         yield b*n**2
%o A204618 A204618_list = list(islice(A204618_gen(),20)) # _Chai Wah Wu_, Jun 22 2022
%Y A204618 Cf. A000110, A070071.
%K A204618 nonn
%O A204618 0,3
%A A204618 _Geoffrey Critzer_, Jan 17 2012