A375949 Expansion of e.g.f. 1 / (4 - 3 * exp(x))^(4/3).

1, 4, 32, 368, 5520, 102064, 2242832, 57095728, 1652211600, 53559908784, 1922581295632, 75700072208688, 3243905700776080, 150289130386531504, 7485459789379535632, 398857142195958963248, 22639650637589839298960, 1363772478150606703714224

Offset: 0

Author

Seiichi Manyama, Sep 03 2024

Keywords

• nonn

Crossrefs

Cf. A032033, A346982, A365558, A375952.

Cf. A005649, A007559, A375948.

Programs

Mathematica

nmax=17; CoefficientList[Series[1 / (4 - 3 * Exp[x])^(4/3),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)

PARI

a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k+1)*stirling(n, k, 2));

Formula

a(n) = Sum_{k=0..n} A007559(k+1) * Stirling2(n,k).

a(n) ~ 3 * sqrt(Pi) * n^(n + 5/6) / (2^(13/6) * Gamma(1/3) * log(4/3)^(n + 4/3) * exp(n)). - Vaclav Kotesovec, Sep 06 2024