A366179 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 + x*A(x)^3/(1 - x).

1, 3, 13, 80, 582, 4627, 38906, 340138, 3060404, 28151835, 263546436, 2502686416, 24048985907, 233410500126, 2284790496700, 22530585455108, 223610524426654, 2231886642819974, 22389017726854323, 225604735477075272, 2282518274913713101

Offset: 0

Author

Seiichi Manyama, Oct 03 2023

Keywords

• nonn

Crossrefs

Partial sums of A366178.

Cf. A364620, A364629, A366180.

Programs

PARI

a(n) = sum(k=0, n, binomial(n+4*k+1, n-k)*binomial(3*k, k)/(2*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n+4*k+1,n-k) * binomial(3*k,k)/(2*k+1).