A375900 E.g.f. satisfies A(x) = 1 / (1 + log(1 - x * A(x)^(1/3)))^3.
1, 3, 21, 237, 3738, 76212, 1912350, 57099816, 1979628552, 78224586240, 3472089084072, 171098204829120, 9271248509444544, 548011290335056272, 35095593433694127696, 2421035179995679335360, 178997036386314294247680, 14121215676864610247122560
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)))/x)^3)) -
PARI
a(n) = 3*sum(k=0, n, (n+k+2)!*abs(stirling(n, k, 1)))/(n+3)!;
Formula
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A052802.
E.g.f.: A(x) = ( (1/x) * Series_Reversion(x * (1 + log(1-x))) )^3.
a(n) = (3/(n+3)!) * Sum_{k=0..n} (n+k+2)! * |Stirling1(n,k)|.