A354738 a(0) = a(1) = 1; a(n) = (n-1) * Sum_{k=0..n-2} a(k) * a(n-k-2).

1, 1, 1, 4, 9, 40, 135, 636, 2688, 13552, 65871, 355520, 1906740, 10963656, 63468171, 386532944, 2383820820, 15294890848, 99626199832, 670333562352, 4583302104450, 32213942456000, 230118463761795, 1683896120829384, 12520330728001670, 95110075114630416

Offset: 0

Author

Ilya Gutkovskiy, Jun 04 2022

Keywords

• nonn

Crossrefs

Cf. A000699, A007477, A185183, A354737.

Programs

Mathematica

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}]
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]

Formula

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