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 A351762 #20 Feb 19 2022 04:42:16
%S A351762 1,2,12,102,1160,16490,281292,5598110,127326096,3257961426,
%T A351762 92625793940,2896747456262,98827517418456,3652643136982970,
%U A351762 145385563800940764,6200097935648462190,282035994269804870432,13631368700936950044578,697586352315912913754916
%N A351762 Expansion of e.g.f. 1/(1 - 2*x*exp(x)).
%F A351762 a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k)^k/k!.
%F A351762 a(0) = 1 and a(n) = 2 * n * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.
%F A351762 a(n) ~ n! / ((1 + LambertW(1/2)) * LambertW(1/2)^n). - _Vaclav Kotesovec_, Feb 19 2022
%o A351762 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*x*exp(x))))
%o A351762 (PARI) a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k)^k/k!);
%o A351762 (PARI) a(n) = if(n==0, 1, 2*n*sum(k=0, n-1, binomial(n-1, k)*a(k)));
%Y A351762 Column k=2 of A351761.
%Y A351762 Cf. A000629, A351777.
%K A351762 nonn
%O A351762 0,2
%A A351762 _Seiichi Manyama_, Feb 18 2022