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 A343672 #7 Jun 20 2022 03:14:34
%S A343672 1,3,19,181,2299,36501,695427,15457709,392672651,11221959685,
%T A343672 356339728243,12446649786429,474273933636411,19577992095770837,
%U A343672 870345573347448803,41455153171478627533,2106173029315813515883,113694251997087087941925,6498401704686168598548435,392062852538564346207533789
%N A343672 a(0) = 1; a(n) = 2 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k).
%F A343672 E.g.f.: 1 / (2 * (1 - x) - exp(x)).
%F A343672 a(n) ~ n! / (2*(1 + LambertW(exp(1)/2)) * (1 - LambertW(exp(1)/2))^(n+1)). - _Vaclav Kotesovec_, Jun 20 2022
%t A343672 a[0] = 1; a[n_] := a[n] = 2 n a[n - 1] + Sum[Binomial[n, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
%t A343672 nmax = 19; CoefficientList[Series[1/(2 (1 - x) - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
%Y A343672 Cf. A000670, A005493, A006155, A032032, A343673, A343674.
%K A343672 nonn
%O A343672 0,2
%A A343672 _Ilya Gutkovskiy_, Apr 25 2021