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A086229
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Determinant of n X n matrix M(i,j) = binomial(2i-1,j), (i,j) ranging from 1 to n.
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2
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1, 1, 3, 20, 280, 8064, 473088, 56229888, 13495173120, 6525665935360, 6348167821918208, 12410090985684467712, 48713743815806763925504, 383714412826047125074739200, 6062249191894029093752222515200
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 2^(n*(n-3)/2)*binomial(2*n, n).
a(n) = 2^C(n,2)*Hypergeometric2F1((1-n)/2,-n/2;1;1).
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MATHEMATICA
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f[n_] := 2^(n (n - 3)/2) Binomial[2 n, n]; (* Or *)
f[n_] := 2^(n (n - 1)/2) Hypergeometric2F1[(1 - n)/2, -n/2, 1, 1]; Array[f, 15, 0] (* Robert G. Wilson v *)
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PROG
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(PARI) a(n) = matdet(matrix(n, n, i, j, binomial(2*i-1, j))); \\ Michel Marcus, Dec 12 2014
(PARI) for(n=0, 30, print1(2^(n*(n-3)/2)*binomial(2*n, n), ", ")) \\ G. C. Greubel, Jan 25 2018
(Magma) [2^(n*(n-3)/2)*Binomial(2*n, n): n in [0..30]]; // G. C. Greubel, Jan 25 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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