From Wouter: in the same Catalanian gist as a few years back :
(2 + k)/((1/2*k*(3 + k))!*(1/2*(-4 + k + k^2))!) + (2 - k)/((1/2*k*(1 + k))!*(1/2*(-4 + 3*k + k^2))!) + 4/((1/2*(-6 + k + k^2))!*(1 + 1/2*k*(3 + k))!) + k/((1/2*(-6 + k + k^2))!*(1 + 1/2*k*(3 + k))!) == k/((1/2*(-2 + k + k^2))!*(1/2*(-2 + 3*k + k^2))!) go figure! W. (c53) factor(minfactorial((2+k)/((k*(3+k)/2)!*((-4+k+k^2)/2)!) +(2-k)/((k*(1+k)/2)!*((-4+3*k+k^2)/2)!) +4/(((-6+k+k^2)/2)!*(1+k*(3+k)/2)!) +k/(((-6+k+k^2)/2)!*(1+k*(3+k)/2)!) = k/(((-2+k+k^2)/2)!*((-2+3*k+k^2)/2)!))); time= 0 msec. 2 2 2 k + k - 6 (d53) 8 k/((k - 1) (k + 2) (k + k - 4) (k + 3 k - 2) (----------)! 2 2 k + 3 k - 4 2 2 (------------)!) = 8 k/((k - 1) (k + 2) (k + k - 4) (k + 3 k - 2) 2 2 2 k + k - 6 k + 3 k - 4 (----------)! (------------)!) 2 2 --rwg