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%I #11 Aug 04 2022 05:35:07
%S 1,37,6229,1454473,393638933,115921649662,36059466046681,
%T 11656478429182365,3876878952705468437,1318042625299425997138,
%U 455984891164728575299354,160005530292143438293125981,56811170133331347049469683481,20372514849857567410065222675568,7367851599324133697992581931476613
%N a(n) = Sum_{k >= 0} binomial(6*n,k)*binomial(3*n,k)*binomial(2*n,k).
%H Mark C. Wilson, <a href="http://www.cs.auckland.ac.nz/~mcw/Research/Outputs/Wils2013.pdf">Diagonal asymptotics for products of combinatorial classes</a>, 2013.
%F 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
%t Table[Sum[Binomial[6n,k]Binomial[3n,k]Binomial[2n,k],{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, May 29 2014 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jun 07 2013