A377530 -id:A377530 - cp's OEIS frontend

A379991 Expansion of e.g.f. exp(-x)/(exp(-x) - x)^3.

1, 5, 34, 293, 3052, 37247, 520918, 8211065, 143997160, 2780465147, 58611713434, 1339236707525, 32969142927580, 869913580853735, 24490615055384062, 732751463209179953, 23217990692393685712, 776689510407852177011, 27353286267329098887202

Offset: 0

Seiichi Manyama, Jan 07 2025

Cf. A377530, A379942, A379990.

a(n) = n!*sum(k=0, n, (k+2)^(n-k)*binomial(k+2, 2)/(n-k)!);

a(n) = n! * Sum_{k=0..n} (k+2)^(n-k) * binomial(k+2,2)/(n-k)!.

A379992 Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^2.

Original entry on oeis.org

1, 1, 7, 41, 349, 3539, 42451, 585605, 9130297, 158692679, 3041499871, 63712004729, 1447946191957, 35479218963083, 932326476195115, 26153289728300909, 779995883104560241, 24644267406802467215, 822278654588440803511, 28891372907012629446881

Offset: 0

Seiichi Manyama, Jan 07 2025

Cf. A358738, A377529, A379933, A379997.

Cf. A368266, A377530, A379994.

With[{nn=20},CoefficientList[Series[Exp[-3x]/(Exp[-x]-x)^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 14 2025 *)

a(n) = n!*sum(k=0, n, (k+1)*(k-1)^(n-k)/(n-k)!);

a(n) = n! * Sum_{k=0..n} (k+1) * (k-1)^(n-k)/(n-k)!.

cp's OEIS Frontend

A379991 Expansion of e.g.f. exp(-x)/(exp(-x) - x)^3.

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