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A138896
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Ratio of (2n-1)! to number of zeros in Sylvester matrix of polynomial of n degree with all nonzero coefficients.
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2
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3, 15, 280, 11340, 798336, 86486400, 13343616000, 2778808032000, 750895681536000, 255454710858547200, 106826515449937920000, 53858368206010368000000, 32215590089995124736000000, 22555515290152300904448000000, 18272974787062050706056806400000, 16959604724241965811558973440000000
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OFFSET
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2,1
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COMMENTS
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(2n-1)! = A009445(n-1) is the number of monomials in determinant of symbolic square matrix of size 2n-1 X 2n-1 without zeros.
Denominators in the series expansion of (1/2)*(Pi/(2*x))^(1/2)* (x*BesselI(1/2, x) - BesselI(3/2, x)). - Abdallah Daddi-Moussa-Ider, Jul 25 2024
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LINKS
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FORMULA
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a(n) = (2*n - 1)!/(2*(n - 1)^2).
Sum_{n=2..oo} 1/a(n) = (1 - 3*e^2 + 8*e*sinh(1))/(4*e) = 0.40366087623617955676434290... . - Stefano Spezia, Jul 25 2024
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MATHEMATICA
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Table[(2 n - 1)!/(2 (n - 1)^2), {n, 2, 20}]
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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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