A365181 G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)^2).

1, 1, 5, 32, 237, 1905, 16160, 142392, 1290613, 11955947, 112697701, 1077438356, 10422562156, 101827196684, 1003312506776, 9958506719664, 99479743121349, 999370184665407, 10090067735619023, 102330789530653912, 1041997707624103589, 10648963961114066129

Offset: 0

Author

Seiichi Manyama, Aug 25 2023

Keywords

• nonn

Crossrefs

Cf. A002294, A365178, A365180, A365182, A365183.

Programs

PARI

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

Formula

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