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%I #32 Jun 21 2021 08:01:55
%S 1,2,8,34,164,878,5136,32490,220476,1594470,12223016,98876322,
%T 840804820,7491247006,69730182720,676390547034,6821988655468,
%U 71398971351510,774032400213336,8677733804696594,100459693769214980,1199306075189097230,14746332963835756400,186534818943430728906
%N a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(n,k) * a(k-1).
%H Georg Fischer, <a href="/A343523/b343523.txt">Table of n, a(n) for n = 0..400</a>
%F G.f. A(x) satisfies: A(x) = 1 + 2 * x * A(x/(1 - x)) / (1 - x)^2.
%t a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 23}]
%t nmax = 23; A[_] = 0; Do[A[x_] = 1 + 2 x A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A001861, A004123, A035009, A040027, A343975, A344735, A344840, A345077, A345078, A345081.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jun 07 2021
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