A370993 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x)) ).
1, 0, 2, 3, 80, 450, 11424, 133140, 3670400, 68303088, 2123212320, 54742984560, 1938915574848, 63653459126400, 2565847637273088, 101718189575664480, 4637150408792355840, 214393171673968519680, 10962579011721928980480, 577166004742408670937600
Offset: 0
Keywords
Programs
-
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x)))/x)) -
PARI
a(n) = sum(k=0, n\2, (n+k)!*abs(stirling(n-k, k, 1))/(n-k)!)/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (n+k)! * |Stirling1(n-k,k)|/(n-k)!.