A365247 G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)^4).

1, 1, 2, 5, 15, 50, 177, 650, 2449, 9412, 36761, 145518, 582556, 2354557, 9594898, 39378259, 162619316, 675258452, 2817643240, 11808576745, 49683880754, 209786559004, 888676860191, 3775654643360, 16084818268474, 68694452578325, 294053067958011

Offset: 0

Author

Seiichi Manyama, Aug 28 2023

Keywords

• nonn

Crossrefs

Cf. A364739, A365246.

Cf. A218251, A364161, A364833.

Programs

PARI

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

Formula

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