A375715 Expansion of e.g.f. 1 / sqrt(1 - x^2 * (exp(x) - 1)).

1, 0, 0, 3, 6, 10, 285, 1911, 8848, 147456, 1818225, 15966775, 244374636, 4105980528, 55574016589, 938220142965, 18765940185840, 342231152117536, 6765035069902833, 154060159512672315, 3469311695227952260, 80672955862303202160, 2068943441492081794101

Offset

0,4

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} A001147(k) * Stirling2(n-2*k,k)/(2^k*(n-2*k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-x^2*(exp(x)-1))))
(PARI) a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = n!*sum(k=0, n\3, a001147(k)*stirling(n-2*k, k, 2)/(2^k*(n-2*k)!));

Crossrefs

Cf. A001147, A358013, A375698.

Sequence in context: A137941 A353998 A355181 * A356951 A355179 A356962

Adjacent sequences: A375712 A375713 A375714 * A375716 A375717 A375718

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2024

Status

approved