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

0,3

Links

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

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.

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 *)

Prog

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

Crossrefs

Cf. A000110, A070071.

Sequence in context: A163003 A368576 A055422 * A289896 A367435 A006887

Adjacent sequences: A204615 A204616 A204617 * A204619 A204620 A204621

Keyword

nonn

Author

Geoffrey Critzer, Jan 17 2012

Status

approved