A375610 Expansion of e.g.f. 1 / (exp(-x) - x^3).

1, 1, 1, 7, 49, 241, 1681, 18481, 192193, 2028097, 26854561, 400419361, 6074016961, 100260498625, 1847840462833, 36061045391281, 738757221740161, 16244778936351361, 380460397886975809, 9341152506044172865, 241084169507148900481, 6559259107807215358081

Offset

0,4

Links

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

Formula

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

a(n) == 1 (mod 6).

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / ((1 + LambertW(1/3)) * 3^(n+4) * exp(n) * LambertW(1/3)^(n+3)). - Vaclav Kotesovec, Aug 21 2024

Prog

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

Crossrefs

Cf. A072597, A352303.

Sequence in context: A207083 A207177 A207089 * A362392 A224150 A094430

Adjacent sequences: A375607 A375608 A375609 * A375611 A375612 A375613

Keyword

nonn

Author

Seiichi Manyama, Aug 21 2024

Status

approved