A354737 - OEIS

A354737

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

1, 1, 2, 6, 20, 80, 336, 1568, 7584, 39312, 210080, 1180256, 6813312, 40890304, 251528704, 1597332480, 10376040448, 69259146752, 472084038144, 3295588345344, 23459477468160, 170610216311808, 1263629972183040, 9543419750909952, 73322350509367296, 573544008429363200

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

FORMULA

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

MATHEMATICA

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}]

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]

CROSSREFS

Cf. A000699, A007477, A185183, A354738.