A379245 G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^2)/(1 - x*A(x)) )^3.

1, 6, 72, 1100, 18984, 352608, 6879152, 139012368, 2884353888, 61091682368, 1315450042368, 28709737064064, 633684940733696, 14120739728984832, 317243001537462528, 7178031348934793472, 163423203504309020160, 3741114809852278047744

Offset: 0

Author

Seiichi Manyama, Dec 18 2024

Keywords

• nonn

Crossrefs

Cf. A365843, A379246.

Cf. A363380, A369215.

Programs

PARI

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

Formula

G.f.: B(x)^3 where B(x) is the g.f. of A363380.

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