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 A383383 #14 Apr 25 2025 12:12:22
%S A383383 1,1,6,26,176,1296,11296,110176,1197696,14304896,186166016,2620022016,
%T A383383 39631568896,640971452416,11034441916416,201411030081536,
%U A383383 3884642996289536,78929236862140416,1684881987266215936,37695662812132212736,881964287274876665856,21536903057742987001856
%N A383383 Expansion of e.g.f. exp(-4*x) / (1-x)^5.
%F A383383 a(n) = n! * Sum_{k=0..n} (-4)^(n-k) * binomial(k+4,4)/(n-k)!.
%F A383383 a(0) = a(1) = 1; a(n) = n*a(n-1) + 4*(n-1)*a(n-2).
%F A383383 a(n) = A383344(n+2)/(4*(n+1)).
%F A383383 a(n) ~ sqrt(2*Pi) * n^(n + 9/2) / (24*exp(n+4)). - _Vaclav Kotesovec_, Apr 25 2025
%o A383383 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-4*x)/(1-x)^5))
%Y A383383 Column k=4 of A383341.
%Y A383383 Cf. A001909, A383381, A383382, A383384.
%K A383383 nonn,easy
%O A383383 0,3
%A A383383 _Seiichi Manyama_, Apr 24 2025