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

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

Mathematica

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

Prog

(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;

Crossrefs

Cf. A004123, A367470, A367471, A375948.

Cf. A001147.

Sequence in context: A243671 A375456 A083304 * A375953 A208248 A290932

Adjacent sequences: A375951 A375952 A375953 * A375955 A375956 A375957

Keyword

nonn

Author

Seiichi Manyama, Sep 03 2024

Status

approved