A365601 Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(2/5).

1, 2, 12, 130, 1990, 39500, 962540, 27807120, 928991280, 35233882320, 1495508048160, 70233555485520, 3615667144284720, 202470393271792800, 12252576455326384800, 796817209624497196800, 55418456683474326892800, 4104671046431448576787200

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} (5*j+2)) * Stirling1(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (5 - 3*k/n) * (k-1)! * binomial(n,k) * a(n-k).

Mathematica

a[n_] := Sum[Product[5*j + 2, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 13 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+2)*stirling(n, k, 1));

Crossrefs

Cf. A347022, A365602, A365603, A365604.

Cf. A365585.

Sequence in context: A079199 A303926 A214759 * A185751 A090361 A258467

Adjacent sequences: A365598 A365599 A365600 * A365602 A365603 A365604

Keyword

nonn

Author

Seiichi Manyama, Sep 11 2023

Status

approved