OFFSET
0,4
COMMENTS
Inverse binomial convolution of the Fubini numbers (A131689).
FORMULA
a(n) = Sum_{k=0..n} (-1)^k * A219859(n,k). - Alois P. Heinz, Jan 24 2022
a(n) = n! * [x^n] (2 - exp(-x))^n. - Fabian Pereyra, Aug 31 2024
MATHEMATICA
a[n_] := Sum[(-1)^(n - k) * Binomial[n, k] * StirlingS2[n, k] * k!, {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, May 10 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*stirling(n, k, 2)*k!); \\ Michel Marcus, May 10 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, May 10 2021
STATUS
approved