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 A368586 #8 Dec 31 2023 10:22:10
%S A368586 0,1,3,6,11,15,36,-42,666,-5499,55705,-611754,7342413,-95449549,
%T A368586 1336296066,-20044437930,320711010756,-5452087178007,98137569210111,
%U A368586 -1864613814984794,37292276299704735,-783137802293788809,17229031650463366448,-396267727960657413354
%N A368586 a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+3,4) / k!.
%F A368586 a(0) = 0; a(n) = -n*a(n-1) + binomial(n+3,4).
%F A368586 E.g.f.: x * (1+3*x/2+x^2/2+x^3/24) * exp(x) / (1+x).
%o A368586 (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 3, binomial(3, k)*x^k/(k+1)!)*exp(x)/(1+x))))
%Y A368586 Cf. A009574, A368585, A368587.
%Y A368586 Cf. A368575.
%K A368586 sign,easy
%O A368586 0,3
%A A368586 _Seiichi Manyama_, Dec 31 2023