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A204618 a(n) = n^2 * B(n) where B(n) are the Bell numbers, A000110. 1
0, 1, 8, 45, 240, 1300, 7308, 42973, 264960, 1712907, 11597500, 82106970, 606757968, 4671909853, 37416267112, 311165672625, 2682916389632, 23947947373356, 220992885195516, 2105619936025577, 20689663294148800, 209417588925127191, 2181250417408504332 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
Sequence in context: A163003 A368576 A055422 * A289896 A367435 A006887
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jan 17 2012
STATUS
approved

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Last modified May 23 14:50 EDT 2024. Contains 372763 sequences. (Running on oeis4.)