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• 55 How many connected graphs over V vertices and E edges?
• 25 Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$
• 23 Compute $\sum_{k=1}^{\infty}e^{-\pi k^2}\left(\pi k^2-\frac{1}{4}\right)$
• 20 Infinite Series $‎\sum\limits_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$
• 20 Sum the series $\sum_{n = 1}^{\infty}\{\coth (n\pi x) + x^{2}\coth(n\pi/x)\}/n^{3}$
• 19 A nice but somewhat challenging binomial identity
• 18 Closed form for $\sum_{n=-\infty}^{\infty}\frac{1}{(n-a)^2+b^2}$.
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