Formula: W_n = integral(0 to pi/2) sin^n(x) dx = integral(0 to pi/2) cos^n(x) dx

For even n = 2m: W_(2m) = [(2m-1)(2m-3)...31] / [2m(2m-2)...42] * pi/2 = [(2m)!/(2^m * m!)^2] * pi/2

For odd n = 2m+1: W_(2m+1) = [2m(2m-2)...42] / [(2m+1)(2m-1)...53]

Quick computation: W_0 = pi/2, W_1 = 1, W_2 = pi/4, W_3 = 2/3, W_4 = 3pi/16, W_5 = 8/15, W_6 = 5pi/32

Wallis' product formula: pi/2 = lim(n->inf) [224466...(2n)(2n)] / [133557...(2n-1)(2n+1)]

Extended Wallis: integral(0 to pi/2) sin^m(x)cos^n(x) dx = B((m+1)/2, (n+1)/2)/2 where B is the Beta function.