OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k) * k! * A010815(k).
MATHEMATICA
m = 21; Range[0, m]! * CoefficientList[Series[Product[1 - (Exp[x] - 1)^k, {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, Jul 08 2020 *)
A010815[k_] := (m = (1 + Sqrt[1 + 24*k])/6; If[IntegerQ[m], (-1)^m, 0] + If[IntegerQ[m - 1/3], (-1)^(m - 1/3), 0]); Table[Sum[StirlingS2[n, k] * k! * A010815[k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 09 2020 *)
PROG
(PARI) N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, 1-(exp(x)-1)^k)))
(PARI) f(n) = if( issquare( 24*n + 1, &n), kronecker( 12, n)); \\ A010815
a(n) = sum(k=0, n, stirling(n, k, 2) * k! * f(k)); \\ Michel Marcus, Jul 09 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 08 2020
STATUS
approved