A376095 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1)^2 * a(k) * a(n-k-1).

1, 1, 5, 54, 983, 26863, 1029188, 52747686, 3491367091, 290276997159, 29639219057133, 3648073361410412, 532858993269296500, 91147584892512564076, 18051321652239427195456, 4098339933686479506696526, 1057506667415381878759070811, 307764793378228160791205354175

Offset: 0

Author

Ilya Gutkovskiy, Sep 10 2024

Keywords

• nonn

Crossrefs

Cf. A000699, A015083, A051893, A088716, A376096, A376097.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(k + 1)^2 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 17}]
nmax = 17; A[] = 0; Do[A[x] = 1 + x A[x]^2 + 3 x^2 A[x] A'[x] + x^3 A[x] A''[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

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