%I #5 Jun 06 2022 02:51:07

%S 1,1,2,6,20,80,336,1568,7584,39312,210080,1180256,6813312,40890304,

%T 251528704,1597332480,10376040448,69259146752,472084038144,

%U 3295588345344,23459477468160,170610216311808,1263629972183040,9543419750909952,73322350509367296,573544008429363200

%N a(0) = a(1) = 1; a(n) = n * Sum_{k=0..n-2} a(k) * a(n-k-2).

%F G.f. A(x) satisfies: A(x) = 1 + x + 2 * x^2 * A(x)^2 + 2 * x^3 * A(x) * A'(x).

%t a[0] = a[1] = 1; a[n_] := a[n] = n Sum[a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 25}]

%t nmax = 25; A[_] = 0; Do[A[x_] = 1 + x + 2 x^2 A[x]^2 + 2 x^3 A[x] D[A[x], x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%Y Cf. A000699, A007477, A185183, A354738.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jun 04 2022