A366266 G.f. A(x) satisfies A(x) = 1 + x + x*A(x)^3.

1, 2, 6, 30, 170, 1050, 6846, 46374, 323154, 2301618, 16680246, 122607342, 911868282, 6849381194, 51885977838, 395941193718, 3040818657954, 23485437201762, 182297207394150, 1421357996034750, 11126867651367498, 87421958424703098, 689130671539597854

Offset: 0

Author

Seiichi Manyama, Oct 06 2023

Keywords

• nonn

Crossrefs

Cf. A025227, A366267, A366268.

Cf. A366221, A366364.

Programs

PARI

a(n) = sum(k=0, n, binomial(2*k+1, n-k)*binomial(3*k, k)/(2*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(2*k+1,n-k) * binomial(3*k,k)/(2*k+1).

a(n) = A366221(n) + A366221(n-1).

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366364.