This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A138896 #32 Aug 19 2025 05:30:40
%S A138896 3,15,280,11340,798336,86486400,13343616000,2778808032000,
%T A138896 750895681536000,255454710858547200,106826515449937920000,
%U A138896 53858368206010368000000,32215590089995124736000000,22555515290152300904448000000,18272974787062050706056806400000,16959604724241965811558973440000000
%N A138896 Ratio of (2n-1)! to number of zeros in Sylvester matrix of polynomial of n degree with all nonzero coefficients.
%C A138896 (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 A138896 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 A138896 a(n) = (2*n - 1)!/(2*(n - 1)^2).
%F A138896 Sum_{n=2..oo} 1/a(n) = (e^2 - 3)/(4*e) = 0.40366087623617955676434290... . - _Stefano Spezia_, Jul 25 2024, simplified by _Vaclav Kotesovec_, Aug 19 2025
%F A138896 Sum_{n>=2} (-1)^n/a(n) = cos(1)/2. - _Amiram Eldar_, Aug 19 2025
%t A138896 Table[(2 n - 1)!/(2 (n - 1)^2), {n, 2, 20}]
%Y A138896 Cf. A001105, A009445, A007878, A138897, A138898.
%K A138896 nonn
%O A138896 2,1
%A A138896 _Artur Jasinski_, Apr 02 2008
%E A138896 a(15)-a(17) from _Stefano Spezia_, Jul 25 2024