A351968 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * a(k) * a(n-3*k-1).

1, 1, 1, 1, 2, 6, 16, 37, 114, 478, 1907, 6777, 28414, 148580, 758930, 3580294, 18982050, 117888762, 720679726, 4193516446, 26798335830, 191775198574, 1353198262531, 9303932353127, 69303156652024, 559295471922890, 4454686099742810, 35198016469190740

Offset: 0

Author

Ilya Gutkovskiy, Feb 26 2022

Keywords

• nonn

Crossrefs

Cf. A138314, A351969.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 3 k] a[k] a[n - 3 k - 1], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 27}]

Formula

E.g.f.: exp( Sum_{n>=0} a(n) * x^(3*n+1) / (3*n+1)! ).