[math-fun] a silly case of factorials

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.