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

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..715

Robert Israel, Linear recurrence of order 10

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).

D-finite with recurrence of order 10 (see link). - Robert Israel, May 08 2026

Prog

(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));

Crossrefs

Cf. A365843, A379246.

Cf. A363380, A369215.

Sequence in context: A052678 A052719 A196882 * A289392 A272688 A379254

Adjacent sequences: A379242 A379243 A379244 * A379246 A379247 A379248

Keyword

nonn

Author

Seiichi Manyama, Dec 18 2024

Status

approved