A375809 Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2)^3.
1, 3, 12, 60, 396, 3240, 30960, 337680, 4152960, 56790720, 853675200, 13990838400, 248242579200, 4739385530880, 96860893409280, 2109714647040000, 48780176949504000, 1193187564259891200, 30781385655513292800, 835194405961256140800
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^3)/x^2)^3)) -
PARI
a(n) = n!*sum(k=0, n\3, (n-3*k+2)!*abs(stirling(n-2*k, n-3*k, 1))/(n-2*k)!)/2;
Formula
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375799.
a(n) = (n!/2) * Sum_{k=0..floor(n/3)} (n-3*k+2)! * |Stirling1(n-2*k,n-3*k)|/(n-2*k)!.