%I #25 Jul 28 2024 00:15:58
%S 3,15,280,11340,798336,86486400,13343616000,2778808032000,
%T 750895681536000,255454710858547200,106826515449937920000,
%U 53858368206010368000000,32215590089995124736000000,22555515290152300904448000000,18272974787062050706056806400000,16959604724241965811558973440000000
%N Ratio of (2n-1)! to number of zeros in Sylvester matrix of polynomial of n degree with all nonzero coefficients.
%C (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.
%C 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
%F a(n) = (2*n - 1)!/(2*(n - 1)^2).
%F Sum_{n=2..oo} 1/a(n) = (1 - 3*e^2 + 8*e*sinh(1))/(4*e) = 0.40366087623617955676434290... . - _Stefano Spezia_, Jul 25 2024
%t Table[(2 n - 1)!/(2 (n - 1)^2), {n, 2, 20}]
%Y Cf. A001105, A009445, A007878, A138897, A138898.
%K nonn
%O 2,1
%A _Artur Jasinski_, Apr 02 2008
%E a(15)-a(17) from _Stefano Spezia_, Jul 25 2024