A376126 a(n) = 1 + Sum_{k=0..n-1} (k+1)^2 * a(k) * a(n-k-1).

1, 2, 11, 127, 2446, 69766, 2758136, 144660949, 9742594594, 820936644105, 84720182796109, 10518406503248799, 1547501158599695053, 266325797207877471893, 53021169588315247959918, 12092601263851930181412631, 3132724961425012148414534036, 914922971820526793968713748093

Offset: 0

Author

Ilya Gutkovskiy, Sep 11 2024

Keywords

• nonn

Crossrefs

Cf. A007317, A321087, A348857, A376095, A376127.

Programs

Mathematica

a[n_] := a[n] = 1 + 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/((1 - x) (1 - x A[x] - 3 x^2 A'[x] - x^3 A''[x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

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