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 A383380 #14 Apr 25 2025 11:49:10
%S A383380 1,2,8,40,248,1808,15136,142784,1496960,17254144,216740864,2945973248,
%T A383380 43065951232,673626675200,11224114860032,198447384666112,
%U A383380 3710328985124864,73136238041563136,1515739708283944960,32947698735175172096,749499782353468522496,17806903161183314378752
%N A383380 Expansion of e.g.f. exp(-2*x) / (1-x)^4.
%F A383380 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A000255.
%F A383380 a(n) = n! * Sum_{k=0..n} (-2)^(n-k) * binomial(k+3,3)/(n-k)!.
%F A383380 a(0) = 1, a(1) = 2; a(n) = (n+1)*a(n-1) + 2*(n-1)*a(n-2).
%F A383380 a(n) ~ sqrt(Pi) * n^(n + 7/2) / (3*sqrt(2)*exp(n+2)). - _Vaclav Kotesovec_, Apr 25 2025
%o A383380 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-2*x)/(1-x)^4))
%Y A383380 Cf. A000261, A383344, A383378.
%Y A383380 Cf. A000023, A052124, A087981, A383381.
%Y A383380 Cf. A000255.
%K A383380 nonn,easy
%O A383380 0,2
%A A383380 _Seiichi Manyama_, Apr 24 2025