A368716 - OEIS

A368716

a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^3 / k!.

0, 1, 6, 9, 28, -15, 306, -1799, 14904, -133407, 1335070, -14684439, 176214996, -2290792751, 32071101258, -481066515495, 7697064252016, -130850092279359, 2355301661034294, -44750731559644727, 895014631192902540, -18795307255050944079

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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^3.

E.g.f.: B_3(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, 3, stirling(3, k, 2)*x^k)*exp(x)/(1+x))))

CROSSREFS

Column k=3 of A368724.

Cf. A048993, A337001, A368585.

Sequence in context: A274977 A340630 A025493 * A091519 A086491 A178597

Adjacent sequences: A368713 A368714 A368715 * A368717 A368718 A368719

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jan 04 2024

STATUS

approved