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 A383384 #21 Sep 04 2025 17:52:58
%S A383384 1,0,5,10,105,620,5725,52950,571025,6686200,85871925,1193029250,
%T A383384 17846277625,285737086500,4874590170125,88245858436750,
%U A383384 1689282139310625,34088182903910000,723088091207873125,16083522103093616250,374280288623526655625,9093957982779894737500
%N A383384 Expansion of e.g.f. exp(-5*x) / (1-x)^5.
%F A383384 a(n) = n! * Sum_{k=0..n} (-5)^(n-k) * binomial(k+4,4)/(n-k)!.
%F A383384 a(n) = (n-1) * (a(n-1) + 5*a(n-2)) for n > 1.
%F A383384 E.g.f.: B(x)^5, where B(x) is the e.g.f. of A000166.
%F A383384 a(n) ~ sqrt(2*Pi) * n^(n + 9/2) / (24*exp(n+5)). - _Vaclav Kotesovec_, Apr 25 2025
%t A383384 With[{nn=30},CoefficientList[Series[Exp[-5x]/(1-x)^5,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 04 2025 *)
%o A383384 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-5*x)/(1-x)^5))
%Y A383384 Column k=5 of A295181.
%Y A383384 Cf. A001909, A383381, A383382, A383383.
%Y A383384 Cf. A000166.
%K A383384 nonn,easy,changed
%O A383384 0,3
%A A383384 _Seiichi Manyama_, Apr 24 2025