Is the following equality true?
$$\sum_i\sum_ja^{ij}\frac{x^iy^j}{i!j!}=e^{x+y}\sum_{i}\sum_j\frac{a^{ij}}{i!j!} $$ where $a$ is not $i,j$-dependent.
2026-03-31 23:25:16.1774999516
Double exponential generating function
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It is not true. The LHS is $e^{a(x+y)}$, and the RHS is $e^{x+y+2a}$.