A365575 Expansion of e.g.f. 1 / (1 + 3 * log(1-x))^(2/3).

1, 2, 12, 114, 1482, 24468, 490020, 11538840, 312363720, 9556741440, 326076452640, 12275391192480, 505400508041760, 22590511357965120, 1089423938332883520, 56379459359942190720, 3116574045158647605120, 183271869976364873222400

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} (3 - k/n) * (k-1)! * binomial(n,k) * a(n-k).

a(n) ~ Gamma(1/3) * n^(n + 1/6) / (3^(1/6) * sqrt(2*Pi) * (exp(1/3) - 1)^(n + 2/3) * exp(2*n/3)). - Vaclav Kotesovec, Nov 11 2023

Mathematica

a[n_] := Sum[Product[3*j + 2, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 11 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 3*j+2)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A347015, A354263.

Sequence in context: A052696 A107723 A258175 * A225797 A302286 A035051

Adjacent sequences: A365572 A365573 A365574 * A365576 A365577 A365578

Keyword

nonn

Author

Seiichi Manyama, Sep 09 2023

Status

approved