A375701 Expansion of e.g.f. 1 / sqrt(1 + x^3 * log(1 - x)).

1, 0, 0, 0, 12, 30, 120, 630, 19152, 166320, 1506600, 14968800, 313014240, 4864860000, 72829607760, 1116874558800, 23605893400320, 495461472105600, 10289649464640000, 215706738207542400, 5222625647551920000, 133507746422859513600, 3481696859911699968000

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)) * |Stirling1(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*log(1-x))))
(PARI) a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+3)*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));

Crossrefs

Cf. A351504, A375699, A375700.

Cf. A375718.

Sequence in context: A320483 A361468 A361467 * A260417 A117313 A080563

Adjacent sequences: A375698 A375699 A375700 * A375702 A375703 A375704

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2024

Status

approved