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

0, 1, 8, 45, 240, 1300, 7308, 42973, 264960, 1712907, 11597500, 82106970, 606757968, 4671909853, 37416267112, 311165672625, 2682916389632, 23947947373356, 220992885195516, 2105619936025577, 20689663294148800, 209417588925127191, 2181250417408504332

Offset: 0

Author

Geoffrey Critzer, Jan 17 2012

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..550

Crossrefs

Cf. A000110, A070071.

Programs

GAP

List([0..22],n->n^2*Bell(n)); # Muniru A Asiru, Apr 20 2019

Mathematica

nn=20;a=Exp[Exp[x]-1];Range[0,nn]!CoefficientList[Series[x D[x D[a,x],x],{x,0,nn}],x]
Table[n^2 BellB[n],{n,0,30}] (* Harvey P. Dale, Jul 01 2022 *)

Python

from itertools import count, accumulate, islice
def A204618_gen(): # generator of terms
    yield 0
    blist, b = (1,), 1
    for n in count(1):
        blist = list(accumulate(blist, initial=(b:=blist[-1])))
        yield b*n**2
A204618_list = list(islice(A204618_gen(),20)) # Chai Wah Wu, Jun 22 2022

Formula

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.