A375813 Expansion of e.g.f. 1/(1 - (exp(x^3) - 1)/x^2)^3.
1, 3, 12, 60, 396, 3240, 30960, 335160, 4072320, 54976320, 815119200, 13152585600, 229441766400, 4303027048320, 86318858545920, 1843929831744000, 41786821607731200, 1001231951502182400, 25288602517469491200, 671488122628741017600
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^3)-1)/x^2)^3)) -
PARI
a(n) = n!*sum(k=0, n\3, (n-3*k+2)!*stirling(n-2*k, n-3*k, 2)/(n-2*k)!)/2;
Formula
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375796.
a(n) = (n!/2) * Sum_{k=0..floor(n/3)} (n-3*k+2)! * Stirling2(n-2*k,n-3*k)/(n-2*k)!.