A371196 Expansion of e.g.f. 1/(1 + x * log(1 - x - x^2)).
1, 0, 2, 9, 56, 570, 5844, 75600, 1101568, 18059328, 330859440, 6657765840, 146394716544, 3488742148320, 89569620370944, 2464853317748640, 72368541315763200, 2258038571305305600, 74611690018599389184, 2602671162733649456640, 95577054989820127994880
Offset: 0
Keywords
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[1/(1+x*Log[1-x-x^2]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 04 2024 *) -
PARI
a(n) = n!*sum(j=0, n, sum(k=0, j, k!*binomial(j, n-j-k)*abs(stirling(j, k, 1))/j!));
Formula
a(n) = n! * Sum_{j=0..n} Sum_{k=0..j} k! * binomial(j,n-j-k) * |Stirling1(j,k)|/j!.