A375954 Expansion of e.g.f. 1 / (3 - 2 * exp(x))^(5/2).

1, 5, 40, 425, 5605, 88100, 1606015, 33291725, 773093830, 19875432575, 560334083965, 17187010139150, 569768238573805, 20299523526975425, 773470729977309040, 31385122689116278325, 1351135296804805544905, 61507193821772778512900

Offset: 0

Author

Seiichi Manyama, Sep 03 2024

Keywords

• nonn

Crossrefs

Cf. A004123, A367470, A367471, A375948.

Cf. A001147.

Programs

Mathematica

nmax=17; CoefficientList[Series[1 / (3 - 2 * Exp[x])^(5/2),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)

PARI

a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k+2)*stirling(n, k, 2))/3;

Formula

a(n) = (1/3) * Sum_{k=0..n} A001147(k+2) * Stirling2(n,k).

a(n) ~ 2^(5/2) * n^(n+2) / (3^(7/2) * log(3/2)^(n + 5/2) * exp(n)). - Vaclav Kotesovec, May 20 2025