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%I #16 Oct 22 2023 08:22:29
%S 393,492872166072,737005538936597762145600,
%T 117847210656873992022720603629873856000,
%U 620630259068078856134953474839665823595181960916480000
%N Number of 7*n X 2*n 0..2 arrays with row sums 2 and column sums 7.
%H R. H. Hardin, <a href="/A172710/b172710.txt">Table of n, a(n) for n = 1..14</a>
%F a(n) = ((2n)!(7n)!/(7!)^(2n)) Sum_{i=0..2n} Sum_{j=0..2n-i} Sum_{k=0..2n-i-j} (21^j*105^(2n-i-j)*(6i+4j+2k+2n)!/(i!j!k!(2n-i-j-k)!(n+2j+k+3i)!*2^(n+2j+k+3i))). - _Shanzhen Gao_, Feb 24 2010
%F a(n) ~ sqrt(Pi) * 7^(12*n + 1/2) * n^(14*n + 1/2) / (2^(n-1) * 3^(4*n) * 5^(2*n) * exp(14*n-3)). - _Vaclav Kotesovec_, Oct 22 2023
%t Table[(2*n)!*(7*n)!/(7!)^(2*n) * Sum[Sum[Sum[(21^j*105^(2*n-i-j)*(6*i+4*j+2*k+2*n)! / (i!*j!*k!*(2*n-i-j-k)!*(n+2*j+k+3*i)! * 2^(n+2*j+k+3*i))), {k,0,2*n-i-j}], {j,0,2*n-i}], {i,0,2*n}], {n,1,12}] (* _Vaclav Kotesovec_, Oct 22 2023 *)
%o (PARI) a(n) = ((2*n)!*(7*n)!/(7!)^(2*n))*sum(i=0, 2*n, sum(j=0, 2*n-i, sum(k=0, 2*n-i-j, (21^j*105^(2*n-i-j)*(6*i+4*j+2*k+2*n)!/(i!*j!*k!*(2*n-i-j-k)!*(n+2*j+k+3*i)!*2^(n+2*j+k+3*i)))))); \\ _Michel Marcus_, Jan 17 2018
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 06 2010
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