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 A367845 #10 Dec 02 2023 13:23:47
%S A367845 1,3,22,250,3816,72968,1675568,44901456,1375306368,47392683648,
%T A367845 1814635323648,76430014409472,3511792144942080,174806087920727040,
%U A367845 9370642040786049024,538202280800536799232,32972397141008692445184,2146270648672407967137792
%N A367845 Expansion of e.g.f. 1/(1 - x + log(1 - 2*x)).
%F A367845 a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 2^k * (k-1)! * binomial(n,k) * a(n-k).
%F A367845 a(n) ~ n! * 2^(n+1) / ((1/LambertW(1/(2*exp(1/2))) - 1 - 2*LambertW(1/(2*exp(1/2)))) * (1 - 2*LambertW(1/(2*exp(1/2))))^n). - _Vaclav Kotesovec_, Dec 02 2023
%o A367845 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 2^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;
%Y A367845 Cf. A052820, A367846, A367847.
%Y A367845 Cf. A367835, A367828.
%K A367845 nonn
%O A367845 0,2
%A A367845 _Seiichi Manyama_, Dec 02 2023