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A138897
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Ratio of (2n-1)! to number of zeros in upper part of Sylvester matrix of polynomial of degree n with all nonzero coefficients.
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1
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3, 20, 420, 18144, 1330560, 148262400, 23351328000, 4940103168000, 1351612226764800, 464463110651904000, 195848611658219520000, 99430833611096064000000, 59828953024276660224000000, 42103628541617628354969600000, 34261827725741345073856512000000, 31923961833867229762934538240000000
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OFFSET
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2,1
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COMMENTS
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If (n,n-1) is the two-part partition of any odd integer greater than 1 then a(n-1) is the number of permutations of shape (n,n-1). For example, the two-part partition of 11 with shape (n,n-1) is (6,5). Pictorially we can draw this as a standard Young diagram with cells populated by hook lengths:
(6,5) = 7 6 5 4 3 1
5 4 3 2 1
and there are a(6-1) = a(5) = 1330560 permutations with shape (6,5). (End)
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LINKS
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FORMULA
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a(n) = (2n - 1)!/(n*(n - 1)) for n >= 2.
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MAPLE
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MATHEMATICA
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Table[(2 n - 1)!/(n (n - 1)), {n, 2, 20}]
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PROG
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(PARI) a(n) = (2*n - 1)!/(n*(n - 1)); \\ Michel Marcus, Oct 28 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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