A368717 a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^4 / k!.

0, 1, 14, 39, 100, 125, 546, -1421, 15464, -132615, 1336150, -14683009, 176216844, -2290790411, 32071104170, -481066511925, 7697064256336, -130850092274191, 2355301661040414, -44750731559637545, 895014631192910900, -18795307255050934419

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^4.

E.g.f.: B_4(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, 4, stirling(4, k, 2)*x^k)*exp(x)/(1+x))))

Crossrefs

Column k=4 of A368724.

Cf. A048993, A337002, A368586.

Sequence in context: A178564 A051866 A162266 * A181149 A019063 A101740

Adjacent sequences: A368714 A368715 A368716 * A368718 A368719 A368720

Keyword

sign

Author

Seiichi Manyama, Jan 04 2024

Status

approved