Is it possible to get an analytical expression as a function of the positive real number $a>1$ for
$$ \sum_{n=1}^\infty \frac{a^n}{n!\sqrt{n}} $$
Is it possible to get an analytical expression as a function of the positive real number $a>1$ for
$$ \sum_{n=1}^\infty \frac{a^n}{n!\sqrt{n}} $$
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