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 A368763 #11 Jan 05 2024 07:55:09
%S A368763 1,2,8,34,156,815,4946,34706,277768,2500077,25000990,275011176,
%T A368763 3300134476,42901748643,600624481562,9009367224110,144149875586576,
%U A368763 2450547884972761,44109861929510838,838087376660707252,16761747533214146580,351996698197497079951
%N A368763 a(n) = n! * (1 + Sum_{k=0..n} binomial(k+2,3) / k!).
%F A368763 a(0) = 1; a(n) = n*a(n-1) + binomial(n+2,3).
%F A368763 a(n) = n! + A368574(n).
%F A368763 E.g.f.: (1 + x * (1+x+x^2/6) * exp(x)) / (1-x).
%o A368763 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x*sum(k=0, 2, binomial(2, k)*x^k/(k+1)!)*exp(x))/(1-x)))
%Y A368763 Cf. A033540, A368762, A368764.
%Y A368763 Cf. A368574, A368767.
%K A368763 nonn
%O A368763 0,2
%A A368763 _Seiichi Manyama_, Jan 04 2024