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 A383382 #14 Apr 25 2025 12:04:46
%S A383382 1,2,9,48,321,2502,22329,223668,2481921,30187242,399071529,5694475608,
%T A383382 87197543361,1425766728942,24787205125209,456477484618908,
%U A383382 8875541469155841,181670665706512722,3904395263350689609,87898121215165479168,2068411075529464370241,50778930934558144895382
%N A383382 Expansion of e.g.f. exp(-3*x) / (1-x)^5.
%F A383382 a(n) = n! * Sum_{k=0..n} (-3)^(n-k) * binomial(k+4,4)/(n-k)!.
%F A383382 a(0) = 1, a(1) = 2; a(n) = (n+1)*a(n-1) + 3*(n-1)*a(n-2).
%F A383382 a(n) ~ sqrt(2*Pi) * n^(n + 9/2) / (24*exp(n+3)). - _Vaclav Kotesovec_, Apr 25 2025
%o A383382 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-3*x)/(1-x)^5))
%Y A383382 Cf. A001909, A383381, A383383, A383384.
%Y A383382 Cf. A010843, A137775, A383378.
%K A383382 nonn,easy
%O A383382 0,2
%A A383382 _Seiichi Manyama_, Apr 24 2025