A365585 Expansion of e.g.f. 1 / (1 + 5 * log(1-x))^(2/5).

1, 2, 16, 214, 4030, 98020, 2923580, 103306320, 4219788720, 195631761360, 10148327972160, 582405469831920, 36635844203963760, 2506613821744700640, 185327181909308762400, 14724431257109269113600, 1251088847268683450630400, 113202071235423519573369600

Offset: 0

Author

Seiichi Manyama, Sep 10 2023

Keywords

• nonn

Crossrefs

Cf. A346987, A365586, A365587, A365588.

Cf. A365568.

Programs

Mathematica

a[n_] := Sum[Product[5*j + 2, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 10 2023 *)

PARI

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

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} (5 - 3*k/n) * (k-1)! * binomial(n,k) * a(n-k).