A365691 G.f. satisfies A(x) = 1 + x^2*A(x)^5 / (1 - x*A(x)).

1, 0, 1, 1, 6, 12, 54, 147, 593, 1886, 7292, 25204, 96153, 348304, 1327716, 4946471, 18936366, 71827598, 276612103, 1062220253, 4115807184, 15947902376, 62148513732, 242485933208, 949828266722, 3726623622402, 14663689944397, 57798199213989

Offset: 0

Author

Seiichi Manyama, Sep 16 2023

Keywords

• nonn

Crossrefs

Cf. A004148, A005043, A025246, A046736, A365690.

Cf. A365693.

Programs

PARI

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

Formula

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