A370941 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + 2*log(1-x)) ).
1, 2, 18, 304, 7668, 259048, 11001968, 563728464, 33857839360, 2333472749376, 181558569560448, 15743501573763456, 1505641080366272640, 157445985444107880960, 17872580693502293022720, 2188829492626563123881472, 287673783237906407512565760
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+2*log(1-x)))/x)) -
PARI
a(n) = sum(k=0, n, 2^k*(n+k)!*abs(stirling(n, k, 1)))/(n+1)!;
Formula
a(n) = (1/(n+1)!) * Sum_{k=0..n} 2^k * (n+k)! * |Stirling1(n,k)|.