Is there any chance of computing the following sum? I have tried a lot of things, yet I didn't manage to get rid of the sum.. Is there any formula?
$$ \sum_{n=1}^\infty \frac {b^n {_1F_1}[n,1,\pi b c] {_2F_2}[{1,n},{n+1,n+1},b]} {2^nn!n}$$
Thanks in advance