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 A368768 #11 Jan 05 2024 07:57:01
%S A368768 1,0,5,0,35,105,756,5082,40986,368379,3684505,40528554,486344013,
%T A368768 6322470349,88514587266,1327718805930,21243500898756,361139515274007,
%U A368768 6500511274938111,123509714223816794,2470194284476344735,51874079974003228809,1141229759428071046448
%N A368768 a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * binomial(k+3,4) / k!).
%F A368768 a(0) = 1; a(n) = n*a(n-1) + (-1)^n * binomial(n+3,4).
%F A368768 a(n) = n! + (-1)^n * A368586(n).
%F A368768 E.g.f.: (1 - x * (1-3*x/2+x^2/2-x^3/24) * exp(-x)) / (1-x).
%o A368768 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*sum(k=0, 3, binomial(3, k)*(-x)^k/(k+1)!)*exp(-x))/(1-x)))
%Y A368768 Cf. A368765, A368766, A368767.
%Y A368768 Cf. A368586, A368764.
%K A368768 nonn
%O A368768 0,3
%A A368768 _Seiichi Manyama_, Jan 04 2024