A368760 a(n) = n! * (1 + Sum_{k=0..n} k^3 / k!).

1, 2, 12, 63, 316, 1705, 10446, 73465, 588232, 5294817, 52949170, 582442201, 6989308140, 90861008017, 1272054114982, 19080811728105, 305292987653776, 5189980790119105, 93419654222149722, 1774973430220851577, 35499468604417039540, 745488840692757839601

Offset

0,2

Links

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

Eric Weisstein's World of Mathematics, Bell Polynomial.

Wikipedia, Touchard polynomials.

Formula

a(0) = 1; a(n) = n*a(n-1) + n^3.

a(n) = n! + A337001(n).

E.g.f.: (1 + B_3(x) * exp(x)) / (1-x), where B_n(x) = Bell polynomials.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1+sum(k=0, 3, stirling(3, k, 2)*x^k)*exp(x))/(1-x)))

Crossrefs

Column k=3 of A368759.

Cf. A337001.

Sequence in context: A361812 A231025 A330387 * A272363 A283488 A006646

Adjacent sequences: A368757 A368758 A368759 * A368761 A368762 A368763

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2024

Status

approved