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A343841
a(n) = Sum{k=0..n} (-1)^(n-k)*binomial(n, k)*Stirling2(n, k).
2
1, 1, -1, -5, 15, 56, -455, -237, 16947, -64220, -529494, 6833608, -8606015, -459331677, 4335744673, 6800310151, -518075832085, 4315086396640, 19931595013738, -812870258798156, 6648395876520816, 46852711038750520, -1752440325584024944, 15485712825845269456
OFFSET
0,4
MAPLE
a := n -> add((-1)^(n-k)*binomial(n, k)*Stirling2(n, k), k=0..n):
seq(a(n), n = 0..24);
MATHEMATICA
a[n_] := Sum[(-1)^(n - k) * Binomial[n, k] * StirlingS2[n, k], {k, 0, n}]; Array[a, 24, 0] (* Amiram Eldar, May 07 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*stirling(n, k, 2)); \\ Michel Marcus, May 07 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, May 04 2021
STATUS
approved