Let $B(n)=(n2)!(n3)!\cdots 1!$ denote the Barnes Gfunction. I am pretty sure that $$ \sum_{m=0}^{k^21} (1)^m\binom{k^21}m \frac{G(k+nm+1)}{G(nm+1)G(k+1)(k^2)!} = n2k^22k $$ when $k$ is odd and is $n\frac 12(k^21)$ when $k$ is even, but I lack a proof. I'd already be happy for some references for identities regarding the Barnes function, as this is all new to me.
