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 A355110 #7 Jun 21 2022 12:46:12
%S A355110 1,2,10,76,768,9696,146896,2596448,52449536,1191944704,30097334784,
%T A355110 835973778432,25330620762112,831497823494144,29394162040580096,
%U A355110 1113330929935101952,44979662118902366208,1930798895281527717888,87756941394038739828736,4210241529540625311727616
%N A355110 Expansion of e.g.f. 2 / (3 - 2*x - exp(2*x)).
%F A355110 a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} binomial(n,k) * 2^(k-1) * a(n-k).
%F A355110 a(n) ~ n! / ((1 + LambertW(exp(3))) * ((3 - LambertW(exp(3)))/2)^(n+1)). - _Vaclav Kotesovec_, Jun 19 2022
%t A355110 nmax = 19; CoefficientList[Series[2/(3 - 2 x - Exp[2 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A355110 a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 2^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
%Y A355110 Cf. A004123, A006155, A007405, A122704, A343672, A355111, A355112, A355113, A355114.
%K A355110 nonn
%O A355110 0,2
%A A355110 _Ilya Gutkovskiy_, Jun 19 2022