A379090 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * (1 + x^3*A(x)^10).

1, 1, 3, 13, 69, 409, 2578, 16883, 113606, 780710, 5457275, 38687680, 277511415, 2010540125, 14690727157, 108136401031, 801111528944, 5968615651663, 44692765261977, 336164201398198, 2538745667960316, 19242953564513454, 146340183680256968, 1116267947369766774

Offset: 0

Author

Seiichi Manyama, Dec 15 2024

Keywords

• nonn

Crossrefs

Cf. A379087.

Programs

PARI

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

Formula

G.f. A(x) satisfies A(x) = exp( 1/3 * Sum_{k>=1} A379087(k) * x^k/k ).

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