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A138896

Ratio of (2n-1)! to number of zeros in Sylvester matrix of polynomial of n degree with all nonzero coefficients.

3, 15, 280, 11340, 798336, 86486400, 13343616000, 2778808032000, 750895681536000, 255454710858547200, 106826515449937920000, 53858368206010368000000, 32215590089995124736000000, 22555515290152300904448000000, 18272974787062050706056806400000, 16959604724241965811558973440000000

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OFFSET

2,1

COMMENTS

(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

LINKS

Table of n, a(n) for n=2..17.

FORMULA

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

MATHEMATICA