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

%I #14 Sep 01 2024 10:13:55

%S 1,2,6,24,144,1080,9360,92400,1038240,13063680,181137600,2744280000,

%T 45145900800,801313793280,15256927445760,310158565516800,

%U 6705376386508800,153609543947059200,3716764672074854400,94715288771578675200,2535525218048030208000

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375796.

%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)! * Stirling2(n-2*k,n-3*k)/(n-2*k)!.

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

%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k+1)!*stirling(n-2*k, n-3*k, 2)/(n-2*k)!);

%Y Cf. A375796, A375813.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 29 2024