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 A383378 #18 Apr 25 2025 12:00:22
%S A383378 1,1,5,21,129,897,7317,67365,692577,7849953,97199109,1304688789,
%T A383378 18863836065,292198665249,4826470920021,84669407740773,
%U A383378 1571901715253313,30786460730863425,634323280633460613,13714611211502376597,310448651226154786881,7342298348439393120321
%N A383378 Expansion of e.g.f. exp(-3*x) / (1-x)^4.
%F A383378 a(n) = n! * Sum_{k=0..n} (-3)^(n-k) * binomial(k+3,3)/(n-k)!.
%F A383378 a(0) = a(1) = 1; a(n) = n*a(n-1) + 3*(n-1)*a(n-2).
%F A383378 a(n) = A137775(n+2)/(3*(n+1)).
%F A383378 a(n) ~ sqrt(2*Pi) * n^(n + 7/2) / (6*exp(n+3)). - _Vaclav Kotesovec_, Apr 25 2025
%o A383378 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-3*x)/(1-x)^4))
%Y A383378 Column k=3 of A383341.
%Y A383378 Cf. A000261, A383344, A383380.
%Y A383378 Cf. A010843, A137775, A383382.
%K A383378 nonn,easy
%O A383378 0,3
%A A383378 _Seiichi Manyama_, Apr 24 2025