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 A352295 #12 Mar 11 2022 08:32:29
%S A352295 1,0,-3,5,29,-181,-401,9645,-14183,-689257,4826171,55700633,
%T A352295 -1024570955,-2770525005,221566919911,-1028838834811,-49439771820367,
%U A352295 723165789334703,9903852025111027,-362150510124039471,-463774017017434739,169793689786411161995
%N A352295 Expansion of e.g.f. 1/(exp(x) - x/(1 + x)).
%F A352295 a(0) = 1; a(n) = Sum_{k=1..n} ((-1)^(k-1) * k! - 1) * binomial(n,k) * a(n-k).
%t A352295 m = 21; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x/(1 + x)), {x, 0, m}], x] (* _Amiram Eldar_, Mar 11 2022 *)
%o A352295 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-x/(1+x))))
%o A352295 (PARI) a(n) = if(n==0, 1, sum(k=1, n, ((-1)^(k-1)*k!-1)*binomial(n, k)*a(n-k)));
%Y A352295 Cf. A352138, A352293, A352294.
%K A352295 sign
%O A352295 0,3
%A A352295 _Seiichi Manyama_, Mar 11 2022