A226307 a(n) = Sum_{k >= 0} binomial(6*n,k)*binomial(3*n,k)*binomial(2*n,k).

1, 37, 6229, 1454473, 393638933, 115921649662, 36059466046681, 11656478429182365, 3876878952705468437, 1318042625299425997138, 455984891164728575299354, 160005530292143438293125981, 56811170133331347049469683481, 20372514849857567410065222675568, 7367851599324133697992581931476613

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Mark C. Wilson, Diagonal asymptotics for products of combinatorial classes, 2013.

Formula

a(n) ~ 2^(6*n) * 3^(9*n-1) / (Pi^(3/2) * n^(3/2) * 5^(5*n - 1/2)). - Vaclav Kotesovec, Aug 04 2022

Mathematica

Table[Sum[Binomial[6n, k]Binomial[3n, k]Binomial[2n, k], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, May 29 2014 *)

Crossrefs

Sequence in context: A183481 A295415 A202801 * A296598 A221034 A221498

Adjacent sequences: A226304 A226305 A226306 * A226308 A226309 A226310

Keyword

nonn

Author

N. J. A. Sloane, Jun 07 2013

Status

approved