( 2n)!/ (2^n * n!)
= { 1*2*3*4*5.*(2n-2)*(2n-1)*(2n) } / { 2^n * 1*2*3*4*.*(n-1)*n }
= { 1*2*3*4*5.*(2n-2)*(2n-1)*(2n) } / { 2*4*6*8*.*(2n-2)*(2n) }
= 1*3*5* .*(2n-1)
证毕