A365114 G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^4.

1, 1, 4, 14, 56, 241, 1080, 4998, 23704, 114588, 562552, 2797138, 14057140, 71288385, 364360204, 1874960408, 9706035408, 50510552881, 264096980192, 1386676113360, 7308650513232, 38654087828310, 205076534841112, 1091144400876394, 5820924498941668

Offset: 0

Author

Seiichi Manyama, Aug 22 2023

Keywords

• nonn

Crossrefs

Cf. A000108, A365113, A365115.

Cf. A321798, A365111.

Programs

PARI

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

Formula

If g.f. satisfies A(x) = 1 + x/(1 - x*A(x))^s, then a(n) = Sum_{k=0..n} binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).