A375689 Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(2/3).

1, 0, 4, 6, 136, 660, 13188, 123480, 2584160, 37044000, 855658800, 16536548160, 428924382720, 10358056051200, 302474317729920, 8701780305254400, 284949736641177600, 9464366170599782400, 345224605512559518720, 12956112412535827353600

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (Product_{j=0..k-1} (3*j+2)) * |Stirling1(n-k,k)|/(n-k)!.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*log(1-x))^(2/3)))
(PARI) a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+2)*abs(stirling(n-k, k, 1))/(n-k)!);

Crossrefs

Cf. A367879, A375688.

Cf. A365575.

Sequence in context: A375697 A377688 A137025 * A377438 A355232 A377685

Adjacent sequences: A375686 A375687 A375688 * A375690 A375691 A375692

Keyword

nonn

Author

Seiichi Manyama, Aug 24 2024

Status

approved