A365732 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^5*A(x)^2).

1, 1, 1, 1, 1, 1, 2, 5, 11, 21, 36, 57, 88, 142, 250, 473, 917, 1751, 3240, 5829, 10350, 18472, 33574, 62293, 117138, 220932, 414777, 773282, 1434776, 2661302, 4955167, 9279325, 17466103, 32971057, 62274094, 117521503, 221572762, 417699772, 788205724, 1489975777

Offset: 0

Author

Seiichi Manyama, Sep 17 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000108, A071879, A364552, A365252.

Cf. A001764, A365734.

Programs

PARI

a(n) = sum(k=0, n\6, binomial(n-5*k, k)*binomial(n-3*k+1, n-5*k)/(n-3*k+1));

Formula

a(n) = Sum_{k=0..floor(n/6)} binomial(n-5*k,k) * binomial(n-3*k+1,n-5*k) / (n-3*k+1) = Sum_{k=0..floor(n/6)} binomial(n-3*k,3*k) * binomial(3*k,k) / (2*k+1).