Is this expression true?

$\displaystyle (n+s)! \Gamma (s+1)= s! \Gamma (n+s+1) $

i was looking at the proof of $\displaystyle J_{-n} (x)= (-1)^n J_n (x) $ and i deduced that expression must be true for the proof provided to be sound, the proof was not from a rigourous source so it may have cut corners & have botched up somewhere.