I recently encountered the following function

$$ f(t) = \sum_{n=0}^\infty \frac{t^{n^2}}{n^2!}. $$

It seems familiar, though I cannot remember where I might have seen it before. I would like to know in what text, if any, it has been studied. Above all, I would like to know its asymptotic properties (how fast it grows) as $t$ tends to infinity ($t$ real and positive).

Thanks,

G.