A368718 a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^5 / k!.

0, 1, 30, 153, 412, 1065, 1386, 7105, -24072, 275697, -2656970, 29387721, -352403820, 4581620953, -64142155518, 962133092145, -15394128425744, 261700184657505, -4710603321945522, 89501463119441017, -1790029262385620340, 37590614510102111241

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Eric Weisstein's World of Mathematics, Bell Polynomial.

Wikipedia, Touchard polynomials

Formula

a(0) = 0; a(n) = -n*a(n-1) + n^5.

E.g.f.: B_5(x) * exp(x) / (1+x), where B_n(x) = Bell polynomials.

Prog

(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, 5, stirling(5, k, 2)*x^k)*exp(x)/(1+x))))

Crossrefs

Column k=5 of A368724.

Cf. A048993, A368587, A368719.

Sequence in context: A206040 A042760 A042762 * A064240 A141221 A159884

Adjacent sequences: A368715 A368716 A368717 * A368719 A368720 A368721

Keyword

sign

Author

Seiichi Manyama, Jan 04 2024

Status

approved