A376393 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-x))^3 ).
1, 3, 33, 669, 20130, 808902, 40799514, 2480325810, 176637134184, 14428585258896, 1330156753687152, 136632403748954088, 15476220160149512160, 1916493979349783418192, 257601843144279267685056, 37352685483321694825767120, 5812026059839341212943591168, 965974072760231560672817681280
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-x))^3)/x)) -
PARI
a(n) = 3*sum(k=0, n, (3*n+k+2)!*abs(stirling(n, k, 1)))/(3*n+3)!;
Formula
E.g.f. A(x) satisfies A(x) = 1/(1 + log(1 - x*A(x)))^3.
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A367139.
a(n) = (3/(3*n+3)!) * Sum_{k=0..n} (3*n+k+2)! * |Stirling1(n,k)|.