Any closed form for this expression?$ \sum_{k=0,\,l=0}^{k=n,\,l=m}\frac{\lambda^{l+k}}{k!\,l!}\sqrt{\frac{n!\,m!}{(n-k)!(m-l)!}}\delta_{n-k,\,m-l}$
$$\frac{\Gamma (m+1) \lambda ^{m-n} \, _1\tilde{F}_1\left(-n;m-n+1;-\lambda ^2\right)}{\sqrt{\Gamma (m+1) \Gamma (n+1)}}$$