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%I #17 Oct 22 2023 08:11:57
%S 1,141,352128,6152037276,467046072593100,115428185943399529200,
%T 76497104228450459248094400,118274738663434470504494036529600,
%U 384184227197088213207839624049360408000,2415977451999318332950627138384873223959560000
%N Number of 3*n X n 0..2 arrays with row sums 2 and column sums 6.
%H R. H. Hardin, <a href="/A172668/b172668.txt">Table of n, a(n) for n = 1..33</a>
%F a(n) = 720^(-n)*n!(3n)! Sum_{i=0..n} Sum_{j=0..n-i} Sum_{k=0..n-i-j} (15^(n-i-k)*45^k*(6i+4j+2k)!/(i!j!k!(n-i-j-k)!(2j+k+3i)!*2^(2j+k+3i))). - _Shanzhen Gao_, Feb 24 2010
%F a(n) ~ sqrt(Pi) * 3^(4*n + 1/2) * n^(6*n + 1/2) / (2^(n-1) * 5^n * exp(6*n - 5/2)). - _Vaclav Kotesovec_, Oct 22 2023
%t Table[720^(-n)*n!*(3*n)! * Sum[Sum[Sum[(15^(n-i-k)*45^k*(6*i+4*j+2*k)! / (i!*j!*k!*(n-i-j-k)!*(2*j+k+3*i)! * 2^(2*j+k+3*i))), {k,0,n-i-j}], {j,0,n-i}], {i,0,n}], {n,1,15}] (* _Vaclav Kotesovec_, Oct 22 2023 *)
%o (PARI) a(n) = 720^(-n)*n!*(3*n)!*sum(i=0, n, sum(j=0, n-i, sum(k=0, n-i-j, (15^(n-i-k)*45^k*(6*i+4*j+2*k)!/(i!*j!*k!*(n-i-j-k)!*(2*j+k+3*i)!*2^(2*j+k+3*i)))))) \\ _Michel Marcus_, Jan 17 2018
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 06 2010
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