A365225 G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^2).

1, 1, 4, 24, 169, 1301, 10605, 89963, 785943, 7023148, 63892489, 589771350, 5509967214, 52001860377, 495048989686, 4748144843341, 45838627944500, 445072967642096, 4343508043479012, 42581707009501604, 419158119684986781, 4141270208611084284

Offset: 0

Author

Seiichi Manyama, Aug 27 2023

Keywords

• nonn

Crossrefs

Cf. A002293, A271469, A349361, A364759, A364866, A365226.

Programs

PARI

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

Formula

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