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 A383381 #13 Apr 25 2025 12:02:53
%S A383381 1,3,14,82,576,4688,43264,445632,5062016,62812288,844863744,
%T A383381 12239474432,189939644416,3142842052608,55223903596544,
%U A383381 1026805938614272,20139224002953216,415503046091767808,8994794537935765504,203848794955954716672,4826475681472562855936,119162892472107134353408
%N A383381 Expansion of e.g.f. exp(-2*x) / (1-x)^5.
%F A383381 a(n) = n! * Sum_{k=0..n} (-2)^(n-k) * binomial(k+4,4)/(n-k)!.
%F A383381 a(0) = 1, a(1) = 3; a(n) = (n+2)*a(n-1) + 2*(n-1)*a(n-2).
%F A383381 a(n) ~ sqrt(2*Pi) * n^(n + 9/2) / (24*exp(n+2)). - _Vaclav Kotesovec_, Apr 25 2025
%o A383381 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-2*x)/(1-x)^5))
%Y A383381 Cf. A001909, A383382, A383383, A383384.
%Y A383381 Cf. A000023, A052124, A087981, A383380.
%K A383381 nonn,easy
%O A383381 0,2
%A A383381 _Seiichi Manyama_, Apr 24 2025