Formula: $W_n$ = integral$\frac{0 to pi}{2}$ $sin^n$(x) dx = integral$\frac{0 to pi}{2}$ $cos^n$(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$\frac{0 to pi}{2}$ $sin^m$(x)$cos^n$(x) dx = B$\frac{(m+1}{2}$, $\frac{n+1}{2}$)/2 where B is the Beta function.