A376087 a(0) = 1; a(n) = Sum_{k=0..n-1} (4*k+1) * a(k) * a(n-k-1).

1, 1, 6, 65, 994, 19386, 456940, 12594465, 396969930, 14078044862, 554782989908, 24053551260186, 1138039204281236, 58353983394380500, 3223791843357228120, 190914111715994215905, 12065701995815379444954, 810602692757305194731094, 57688894099612173692496580

Offset: 0

Author

Ilya Gutkovskiy, Sep 09 2024

Keywords

• nonn

Crossrefs

Cf. A000699, A088716, A151403, A215648, A375393, A376086.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(4 k + 1) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[] = 0; Do[A[x] = 1 + x A[x]^2 + 4 x^2 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 + 4 * x^2 * A'(x) * A(x).