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%I #6 Nov 06 2021 09:07:27
%S 1,2,3,12,26,125,317,1642,4492,24188,69174,381613,1123923,6304781,
%T 18962485,107682542,329007674,1885923378,5833166568,33685017384,
%U 105214504816,611241171298,1924588709710,11236434464097,35617302886643,208815253200975,665665428686531
%N G.f. A(x) satisfies: A(x) = 1 + x * A(-x) / (1 - x) + x * A(x)^2.
%F a(0) = 1; a(n) = Sum_{k=0..n-1} a(k) * ((-1)^k + a(n-k-1)).
%t nmax = 26; A[_] = 0; Do[A[x_] = 1 + x A[-x]/(1 - x) + x A[x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = Sum[a[k] ((-1)^k + a[n - k - 1]), {k, 0, n - 1}]; Table[a[n], {n, 0, 26}]
%Y Cf. A000108, A073157, A215973, A349014, A349015.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Nov 05 2021
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