A379992 Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^2.
1, 1, 7, 41, 349, 3539, 42451, 585605, 9130297, 158692679, 3041499871, 63712004729, 1447946191957, 35479218963083, 932326476195115, 26153289728300909, 779995883104560241, 24644267406802467215, 822278654588440803511, 28891372907012629446881
Offset: 0
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[Exp[-3x]/(Exp[-x]-x)^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 14 2025 *) -
PARI
a(n) = n!*sum(k=0, n, (k+1)*(k-1)^(n-k)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} (k+1) * (k-1)^(n-k)/(n-k)!.