A367425 Expansion of e.g.f. 1 / (1 + log(1 - 3*x))^(2/3).

1, 2, 16, 206, 3634, 81308, 2203300, 70110920, 2562224200, 105749169920, 4864704955360, 246809377578080, 13690337856245920, 824235763862751680, 53528771980276233280, 3730024030461061339520, 277598358023069362894720, 21975673266870666302685440

Offset: 0

Author

Seiichi Manyama, Nov 18 2023

Keywords

• nonn

Crossrefs

Cf. A367428.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[1/(1+Log[1-3x])^(2/3),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 16 2024 *)

PARI

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

Formula

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

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