%I #4 Jun 06 2022 02:51:33

%S 1,1,1,4,9,40,135,636,2688,13552,65871,355520,1906740,10963656,

%T 63468171,386532944,2383820820,15294890848,99626199832,670333562352,

%U 4583302104450,32213942456000,230118463761795,1683896120829384,12520330728001670,95110075114630416

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

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

%t a[0] = a[1] = 1; a[n_] := a[n] = (n - 1) 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 + 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, A354737.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Jun 04 2022