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 A383344 #16 Apr 25 2025 12:10:52
%S A383344 1,0,4,8,72,416,3520,31104,316288,3525632,43117056,572195840,
%T A383344 8191304704,125761056768,2060841582592,35894401335296,662066514984960,
%U A383344 12890305925218304,264155723747688448,5682905054074109952,128051031032232411136,3015653024970577018880
%N A383344 Expansion of e.g.f. exp(-4*x) / (1-x)^4.
%F A383344 a(n) = n! * Sum_{k=0..n} (-4)^(n-k) * binomial(k+3,3)/(n-k)!.
%F A383344 a(n) = (n-1) * (a(n-1) + 4*a(n-2)) for n > 1.
%F A383344 E.g.f.: B(x)^4, where B(x) is the e.g.f. of A000166.
%F A383344 a(n) ~ sqrt(2*Pi) * n^(n + 7/2) / (6*exp(n+4)). - _Vaclav Kotesovec_, Apr 25 2025
%o A383344 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-4*x)/(1-x)^4))
%Y A383344 Column k=4 of A295181.
%Y A383344 Cf. A000166, A087981, A137775.
%Y A383344 Cf. A088991, A381504.
%K A383344 nonn,easy
%O A383344 0,3
%A A383344 _Seiichi Manyama_, Apr 23 2025