A365193 G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)^3).

1, 1, 6, 49, 463, 4760, 51702, 583712, 6781774, 80555066, 973813974, 11941861079, 148191437719, 1857464450449, 23481830726334, 299056887494427, 3833349330581255, 49416395972195630, 640256115370243620, 8332835556325119938, 108890550249605779116

Offset: 0

Author

Seiichi Manyama, Aug 25 2023

Keywords

• nonn

Crossrefs

Cf. A002295, A243667, A349332, A364748, A365192, A365194.

Cf. A365187.

Programs

PARI

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

Formula

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