A375951 Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^(5/3).

1, 5, 45, 570, 9270, 183840, 4299360, 115795920, 3528915840, 120032889840, 4507313333040, 185185602462240, 8262852630732000, 397873645339668480, 20563762111640910720, 1135441077379757372160, 66703342626913255770240, 4154100873615633462894720

Offset: 0

Author

Seiichi Manyama, Sep 03 2024

Keywords

• nonn

Crossrefs

Cf. A354263, A365575, A375946.

Cf. A008544.

Programs

Mathematica

nmax=17; CoefficientList[Series[1 / (1 + 3 * Log[1-x])^(5/3),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)

PARI

a008544(n) = prod(k=0, n-1, 3*k+2);
a(n) = sum(k=0, n, a008544(k+1)*abs(stirling(n, k, 1)))/2;

Formula

a(n) = (1/2) * Sum_{k=0..n} A008544(k+1) * |Stirling1(n,k)|.