A379996 Expansion of e.g.f. exp(-x)/(exp(-x) - x)^4.

1, 7, 61, 639, 7825, 109683, 1731645, 30403495, 587595649, 12395233539, 283385424829, 6979650164391, 184235963026833, 5188528445210035, 155284012799863453, 4921569063327156807, 164672737994453759617, 5800532536265417597571, 214559605389429001486557

Offset: 0

Author

Seiichi Manyama, Jan 07 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A379943, A379993, A379994, A379995.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[-x]/(Exp[-x]-x)^4,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 19 2025 *)

PARI

a(n) = n!*sum(k=0, n, (k+3)^(n-k)*binomial(k+3, 3)/(n-k)!);

Formula

a(n) = n! * Sum_{k=0..n} (k+3)^(n-k) * binomial(k+3,3)/(n-k)!.