A375665 - OEIS

%I #10 Sep 01 2024 09:35:06

%S 1,0,0,18,0,180,4320,2520,241920,3674160,12700800,599749920,

%T 7903526400,77863705920,2660390853120,37269497865600,683129089843200,

%U 19948163057222400,339567800885913600,8690022866119795200,241333983478748160000,5217670959100125926400

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

%F E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375588.

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2))^3))

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

%Y Cf. A375588, A375664.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Aug 23 2024