A375718 Expansion of e.g.f. 1 / sqrt(1 - x^3 * (exp(x) - 1)).

1, 0, 0, 0, 12, 30, 60, 105, 15288, 136332, 794160, 3742695, 165156420, 2977295178, 34259966832, 307175369865, 8066201665200, 210501545175960, 3893163654156768, 56023707973290507, 1275541469736173820, 38629328708426716470, 991445561747177496960

Offset

0,5

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (Product_{j=0..k-1} (6*j+3)) * Stirling2(n-3*k,k)/(6^k*(n-3k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-x^3*(exp(x)-1))))
(PARI) a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+3)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));

Crossrefs

Cf. A358014, A375716, A375717.

Cf. A375701.

Sequence in context: A084699 A323441 A064483 * A365277 A322181 A334791

Adjacent sequences: A375715 A375716 A375717 * A375719 A375720 A375721

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2024

Status

approved