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
Keywords
Programs
-
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)!);
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)!.