A375810 - OEIS

%I #12 Sep 01 2024 10:13:59

%S 1,2,6,30,192,1480,13500,141540,1676640,22141728,322388640,5130084960,

%T 88561408320,1648294876800,32898981155040,700940855815200,

%U 15877318955097600,380996919471168000,9654670629548904960,257627854786123261440,7220676423560766566400

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

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^2)-1)/x)^2))

%o (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*stirling(n-k, n-2*k, 2)/(n-k)!);

%Y Cf. A375795, A375811.

%Y Cf. A375664.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 29 2024