some monstrosities

\prod_{a,b,c=1}^{\infty} \sum_{n=1}^{\infty} \frac{1}{n^{an^{2}+bn+c}}

and also, say:

\prod_{a,b=1}^{\infty} \sum_{n=1}^{\infty} \frac{1}{n^{an+b}}

and also, whittling away:

\prod_{a=1}^{\infty} \sum_{n=1}^{\infty} \frac{1}{n^{an}} \approx 1.40259533132089773624198314053114268659737197392761\ldots

(the last used an evaluation by mpmath:

>>> mp.dps=50
>>> nprod(lambda a: nsum(lambda n: 1/(n**(a*n)), [1,inf]), [1, inf])
mpf(‘1.40259533132089773624198314053114268659737197392761’)

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