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A172651
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Number of 2*n X n 0..2 arrays with row sums 2 and column sums 4.
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1
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1, 19, 2385, 1093050, 1328792850, 3536978063850, 18126466426218150, 163081394186253543000, 2402820978940192425615000, 54918587341306311174536985000, 1864314763102041137068549803435000
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 24^(-n)*n!(2n)!*Sum_{i=0..n} Sum_{j=0..n-i} (3^(n-i-j)6^j*(4i+2j)!/(i!j!(n-i-j)!(2i+j)!2^(2i+j))). - Shanzhen Gao, Feb 24 2010
a(n) ~ sqrt(Pi) * 2^(3*n + 3/2) * n^(4*n + 1/2) / (3^n * exp(4*n - 3/2)). - Vaclav Kotesovec, Oct 22 2023
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MATHEMATICA
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Table[24^(-n)*n!*(2*n)! * Sum[Sum[(3^(n-i-j)*6^j*(4*i+2*j)! / (i!*j!*(n-i-j)!*(2*i+j)!*2^(2*i+j))), {j, 0, n-i}], {i, 0, n}], {n, 1, 15}] (* Vaclav Kotesovec, Oct 22 2023 *)
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PROG
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(PARI) a(n) = 24^(-n)*n!*(2*n)!*sum(i=0, n, sum(j=0, n-i, (3^(n-i-j)*6^j*(4*i+2*j)!/(i!*j!*(n-i-j)!*(2*i+j)!*2^(2*i+j))))); \\ Michel Marcus, Jan 17 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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