A375950 Expansion of e.g.f. 1 / (5 - 4 * exp(x))^(3/2).

1, 6, 66, 1026, 20586, 505746, 14698506, 493198866, 18762818826, 797986018386, 37518173169546, 1932228677052306, 108176937646278666, 6541409475478588626, 424885004809917954186, 29502494166061176035346, 2180808897487960097444106

Offset: 0

Author

Seiichi Manyama, Sep 03 2024

Keywords

• nonn

Crossrefs

Cf. A000407, A354242, A375947.

Programs

Mathematica

nmax=16; CoefficientList[Series[1 / (5 - 4 * Exp[x])^(3/2),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)

PARI

a000407(n) = (2*n+1)!/n!;
a(n) = sum(k=0, n, a000407(k)*stirling(n, k, 2));

Formula

a(n) = Sum_{k=0..n} A000407(k) * Stirling2(n,k).