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 A368766 #17 Mar 26 2025 10:44:44
%S A368766 1,0,3,3,22,95,591,4109,32908,296127,2961325,32574509,390894186,
%T A368766 5081624327,71142740683,1067141110125,17074257762136,290262381956159,
%U A368766 5224722875211033,99269734629009437,1985394692580188950,41693288544183967719,917252347972047290071
%N A368766 a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * binomial(k+1,2) / k!).
%H A368766 Harvey P. Dale, <a href="/A368766/b368766.txt">Table of n, a(n) for n = 0..449</a>
%F A368766 a(0) = 1; a(n) = n*a(n-1) + (-1)^n * binomial(n+1,2).
%F A368766 a(n) = n! + (-1)^n * A009574(n).
%F A368766 E.g.f.: (1 - x * (1-x/2) * exp(-x)) / (1-x).
%t A368766 nxt[{n_,a_}]:={n+1,a(n+1)+(-1)^(n+1) Binomial[n+2,2]}; NestList[nxt,{0,1},30][[;;,2]] (* _Harvey P. Dale_, Mar 26 2025 *)
%o A368766 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*sum(k=0, 1, binomial(1, k)*(-x)^k/(k+1)!)*exp(-x))/(1-x)))
%Y A368766 Cf. A368765, A368767, A368768.
%Y A368766 Cf. A009574, A368762.
%K A368766 nonn
%O A368766 0,3
%A A368766 _Seiichi Manyama_, Jan 04 2024