How to sum of this mass density function? Let $X$ and $Y$ have joint mass function
$f(j,k)=\frac {c(j+k)a^{j+k}}{j!k!}$,  $j,k\geq 0$
where $a$ is a constant. Find $c$
This sum seems hard to to. How to complete this sum?

Hint:  It looks like $\frac c{j!k!} \frac d{da} a^{j+k+1}$ so binomial identities have a lot to say.
