A365250 G.f. satisfies A(x) = 1 + x*A(x)^3/(1 - x^2*A(x)^6).

1, 1, 3, 13, 67, 379, 2271, 14158, 90875, 596506, 3985661, 27018149, 185356123, 1284502886, 8978432666, 63225825415, 448131632123, 3194452061366, 22886882317758, 164718040282975, 1190311371951321, 8633251770618136, 62825467894307447

Offset: 0

Author

Seiichi Manyama, Aug 28 2023

Keywords

• nonn

Crossrefs

Cf. A101785, A365246.

Cf. A002293.

Programs

Mathematica

a[n_]:=Sum[Binomial[n-k-1,k]*Binomial[3*n+1,n-2*k],{k,0,Floor[n/2]}]/(3*n+1); Table[a[n],{n,0,22}] (* Robert P. P. McKone, Aug 29 2023 *)

PARI

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

Formula

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