[math-fun] pi number

u_(n+1)=sqrt(2+2*u_(n))/2; u_(0)=-1; a_(n)=2^(k*(2*n+1))*sum((k!/((i!)*(k-i)!))*(-1)^(i)*u_(n)^i,i,0,k); n--- infinity; a_(n)---Pi^(2*k);