A375686 Expansion of e.g.f. 1 / (1 + x^2/2 * log(1 - x))^3.

1, 0, 0, 9, 18, 60, 1350, 9072, 65520, 984960, 11627280, 135883440, 2109317760, 33214821120, 529403146272, 9536973415200, 182108114697600, 3599078480524800, 76130266179974400, 1701744508586747520, 39652022068801632000, 970411293528131750400

Offset

0,4

Links

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A351505.

a(n) = (n!/2) * Sum_{k=0..floor(n/3)} (k+2)! * |Stirling1(n-2*k,k)|/(2^k*(n-2*k)!).

Prog

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

Crossrefs

Cf. A351505, A375685.

Cf. A375682.

Sequence in context: A107313 A232921 A295473 * A255839 A361082 A166640

Adjacent sequences: A375683 A375684 A375685 * A375687 A375688 A375689

Keyword

nonn

Author

Seiichi Manyama, Aug 24 2024

Status

approved