A379089 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * (1 + x^3*A(x)^7).

1, 1, 2, 6, 24, 108, 503, 2385, 11537, 56992, 286769, 1464317, 7564803, 39457205, 207500615, 1099066181, 5858206629, 31399478619, 169132215962, 915057263082, 4970445985138, 27095859218337, 148193424618950, 812923791698402, 4471543767583949, 24657936277287687

Offset: 0

Author

Seiichi Manyama, Dec 15 2024

Keywords

• nonn

Crossrefs

Cf. A379085.

Programs

PARI

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

Formula

G.f. A(x) satisfies A(x) = exp( 1/2 * Sum_{k>=1} A379085(k) * x^k/k ).

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