A377790 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - 3*log(1-x)) ).
1, 3, 21, 249, 4302, 98982, 2860686, 99779418, 4081683744, 191696903424, 10168315038360, 601321398385320, 39230551252853424, 2799199551778309872, 216856533870111053520, 18127987493141612555280, 1626479163148212406506240, 155902932291162161594016000
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1-3*log(1-x)))/x)) -
PARI
a(n) = n!*sum(k=0, n, 3^k*abs(stirling(n, k, 1))/(n-k+1)!);
Formula
a(n) = n! * Sum_{k=0..n} 3^k * |Stirling1(n,k)|/(n-k+1)!.