A366177 G.f. A(x) satisfies A(x) = 1/(1 - x) + x*A(x)^3/(1 - x)^2.

1, 2, 9, 55, 382, 2866, 22648, 185722, 1565725, 13486036, 118163960, 1049908872, 9437623630, 85671158757, 784247925911, 7231502249005, 67106161264660, 626221543735984, 5872908642398977, 55323451127462123, 523240983692525619, 4966658879361416551

Offset: 0

Author

Seiichi Manyama, Oct 03 2023

Keywords

• nonn

Crossrefs

Partial sums give A364620.

Cf. A199475, A346626, A366178.

Programs

PARI

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

Formula

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