A375810 Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x)^2.

1, 2, 6, 30, 192, 1480, 13500, 141540, 1676640, 22141728, 322388640, 5130084960, 88561408320, 1648294876800, 32898981155040, 700940855815200, 15877318955097600, 380996919471168000, 9654670629548904960, 257627854786123261440, 7220676423560766566400

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375795.

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^2)-1)/x)^2))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*stirling(n-k, n-2*k, 2)/(n-k)!);

Crossrefs

Cf. A375795, A375811.

Cf. A375664.

Sequence in context: A353982 A340243 A373659 * A375806 A078700 A176719

Adjacent sequences: A375807 A375808 A375809 * A375811 A375812 A375813

Keyword

nonn

Author

Seiichi Manyama, Aug 29 2024

Status

approved