This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379996 #9 May 19 2025 12:44:29
%S A379996 1,7,61,639,7825,109683,1731645,30403495,587595649,12395233539,
%T A379996 283385424829,6979650164391,184235963026833,5188528445210035,
%U A379996 155284012799863453,4921569063327156807,164672737994453759617,5800532536265417597571,214559605389429001486557
%N A379996 Expansion of e.g.f. exp(-x)/(exp(-x) - x)^4.
%F A379996 a(n) = n! * Sum_{k=0..n} (k+3)^(n-k) * binomial(k+3,3)/(n-k)!.
%t A379996 With[{nn=20},CoefficientList[Series[Exp[-x]/(Exp[-x]-x)^4,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 19 2025 *)
%o A379996 (PARI) a(n) = n!*sum(k=0, n, (k+3)^(n-k)*binomial(k+3, 3)/(n-k)!);
%Y A379996 Cf. A379943, A379993, A379994, A379995.
%K A379996 nonn,easy
%O A379996 0,2
%A A379996 _Seiichi Manyama_, Jan 07 2025