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A172678
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Number of 4*n X n 0..2 arrays with row sums 2 and column sums 8
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1
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1, 1107, 57775905, 40629560387130, 203571289613781911250, 4937928427617947420104982250, 447362835296127429187676764430583750, 125661678519106774927206307245894357500775000
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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) = (1/(8!)^n)*Sum_(v=0..n} Sum_{m=0..n-v} Sum_{g=0..n-v-m} Sum_{b=0..n-v-m-g} (28^b*210^g*420^m*105^v*n!(4n)!(8n-2b-4g-6m-8v)!)/((n-b-g-m-v)!b!g!m!v!(4n-b-2g-3m-4v)!2^(4n-b-2g-3m-4v)). - Shanzhen Gao, Feb 25 2010
a(n) ~ sqrt(Pi) * 2^(13*n+2) * n^(8*n + 1/2) / (3^(2*n) * 5^n * 7^n * exp(8*n - 7/2)). - Vaclav Kotesovec, Oct 22 2023
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MATHEMATICA
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Table[1/(8!)^n * Sum[Sum[Sum[Sum[(28^b*210^g*420^m*105^v*n!*(4*n)! * (8*n-2*b-4*g-6*m-8*v)!) / ((n-b-g-m-v)! * b!*g!*m!*v! * (4*n-b-2*g-3*m-4*v)! * 2^(4*n-b-2*g-3*m-4*v)), {b, 0, n-v-m-g}], {g, 0, n-v-m}], {m, 0, n-v}], {v, 0, n}], {n, 1, 12}] (* Vaclav Kotesovec, Oct 22 2023 *)
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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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