The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #5 Sep 10 2024 00:22:40
%S 1,2,14,160,2444,45792,1005480,25169760,705321200,21841420384,
%T 740194188032,27243674154368,1082259310732096,46159435144505600,
%U 2104195645965319680,102113572703197079040,5256795948307255075584,286171738279517073904128,16427146596936396844976640
%N a(0) = 1; a(n) = Sum_{k=0..n-1} (3*k+2) * a(k) * a(n-k-1).
%F G.f. A(x) satisfies: A(x) = 1 + 2 * x * A(x)^2 + 3 * x^2 * A'(x) * A(x).
%t a[0] = 1; a[n_] := a[n] = Sum[(3 k + 2) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
%t nmax = 18; A[_] = 0; Do[A[x_] = 1 + 2 x A[x]^2 + 3 x^2 A'[x] A[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A000699, A005159, A088716, A215648, A375393, A376087.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Sep 09 2024