A375952 Expansion of e.g.f. 1 / (4 - 3 * exp(x))^(5/3).

1, 5, 45, 565, 9085, 177925, 4106445, 109105365, 3279219485, 109983317925, 4071784884845, 164919693538165, 7253726995805885, 344284133391481925, 17538600019076063245, 954467594134586386965, 55263075631036363208285, 3391909484128563111709925

Offset: 0

Author

Seiichi Manyama, Sep 03 2024

Keywords

• nonn

Crossrefs

Cf. A032033, A346982, A365558, A375949.

Cf. A008544.

Programs

Mathematica

nmax=17; CoefficientList[Series[1 / (4 - 3 * Exp[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)*stirling(n, k, 2))/2;

Formula

a(n) = (1/2) * Sum_{k=0..n} A008544(k+1) * Stirling2(n,k).