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 A368765 #16 Mar 26 2025 11:42:51
%S A368765 1,0,2,3,16,75,456,3185,25488,229383,2293840,25232229,302786760,
%T A368765 3936227867,55107190152,826607852265,13225725636256,224837335816335,
%U A368765 4047072044694048,76894368849186893,1537887376983737880,32295634916658495459,710503968166486900120,16341591267829198702737
%N A368765 a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * k / k!).
%F A368765 a(0) = 1; a(n) = n*a(n-1) + (-1)^n * n.
%F A368765 a(n) = n! - A000240(n).
%F A368765 E.g.f.: (1 - x * exp(-x)) / (1-x).
%F A368765 a(n) ~ (1 - exp(-1)) * n!. - _Vaclav Kotesovec_, Jan 13 2024
%t A368765 Table[n!(1+Sum[(-1)^k k/k!,{k,0,n}]),{n,0,30}] (* _Harvey P. Dale_, Mar 26 2025 *)
%o A368765 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*exp(-x))/(1-x)))
%Y A368765 Cf. A368766, A368767, A368768.
%Y A368765 Cf. A000240, A033540.
%K A368765 nonn
%O A368765 0,3
%A A368765 _Seiichi Manyama_, Jan 04 2024