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A093527
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Denominators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk.
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7
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1, 1, 3, 2, 5, 1, 7, 4, 9, 5, 11, 3, 13, 7, 1, 8, 17, 3, 19, 1, 7, 11, 23, 2, 25, 13, 27, 1, 29, 15, 31, 16, 11, 17, 5, 9, 37, 19, 39, 2, 41, 1, 43, 11, 1, 23, 47, 4, 49, 25, 17, 13, 53, 9, 55, 7, 19, 29, 59, 5, 61, 31, 21, 32, 13, 1, 67, 17, 23, 7, 71, 2, 73, 37, 5, 19, 1, 13, 79
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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(k) = Denominator[(2*Gamma[3 + n])/((2 + n)*Gamma[2 + n/2]*Gamma[3 + n/2])] for n = 2k.
a(n) = numerator((n+1)(n+2)/binomial(2(n+1), n+1));
a(n) = numerator(2*binomial(n+2, 2)/binomial(2(n+1), n+1)). (End)
a(n) = numerator((n+1)/C(n+1)). - Paul Barry, Nov 17 2004
a(n) = denominator((n + 2)*binomial(2*n+3, n+1)/((n + 1)*(2*n + 3))). - Stefano Spezia, Aug 06 2022
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EXAMPLE
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1, 128/(45*Pi), 1, 2048/(525*Pi), 5/3, 16384/(2205*Pi), ...
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MAPLE
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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