A365758 G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^4*A(x)^5).

1, 1, 1, 1, 1, 2, 8, 29, 85, 212, 481, 1081, 2627, 7100, 20328, 58023, 160430, 430391, 1140892, 3051678, 8334638, 23199896, 65148939, 182781853, 510225082, 1419091293, 3948954920, 11034704856, 31001204632, 87466532564, 247303929326, 699572256145

Offset: 0

Author

Seiichi Manyama, Sep 18 2023

Keywords

• nonn

Crossrefs

Cf. A023427, A112805, A212384, A365245.

Cf. A215342, A365760.

Programs

PARI

a(n) = sum(k=0, n\4, binomial(n-3*k-1, k)*binomial(n+k+1, n-4*k)/(n+k+1));

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k-1,k) * binomial(n+k+1,n-4*k) / (n+k+1).