A379088 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * (1 + x^2*A(x)^7).

1, 1, 4, 23, 153, 1106, 8443, 66977, 546688, 4561527, 38732871, 333607557, 2907549308, 25594629702, 227233349522, 2032335895221, 18294192036084, 165612099597170, 1506797883831078, 13771122728779086, 126368176338669841, 1163834520126009000, 10754353177914306483

Offset: 0

Author

Seiichi Manyama, Dec 15 2024

Keywords

• nonn

Crossrefs

Cf. A379086.

Programs

PARI

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

Formula

G.f. A(x) satisfies A(x) = exp( 1/3 * Sum_{k>=1} A379086(k) * x^k/k ).

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