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Important formulas in combinatorics

A hard integral identity on MATH.SE

Why does $d^n \exp(-x-x^{-1})/(dx)^n$ only have $n$ positive real zeroes?

A strengthening of the Cauchy-Schwarz inequality

Solve in positive integers: $n!=m(m+1)$

Finding a path through real rooted polynomials

Mysterious symmetry - in search for a bijection

A new way of approaching the pole of the Riemann zeta function - and a new conjectured formula

The function $\sum_{0}^{\infty} x^n/n^n$

An explicit series representation for the analytic tetration with complex height

Symmetric strengthening of the Cauchy-Schwarz inequality

$\binom{x}{2}+\binom{x}{4}+\cdots+\binom{x}{2u}$ is a convex function on $[0,+\infty)$?

Number of collinear ways to fill a grid

Do these polynomials have alternating coefficients?

Are surjections $[n]\to [k]$ more common than injections $[k]\to [n]$?

A question related to Hofstadter-Conway \$10000 sequence

Does the mean ratio of the perimeter to the hypotenuse of right triangles converge to $1 + \dfrac{4}{\pi}$?

A conjecture harmonic numbers

A conjecture of Littlewood

More mysteries about the zeros of the Riemann zeta function

Fourier transform of $f_a(x)= a^{-2}\exp(-|x|^a)$, $a \in (0,2)$, is decreasing in $a$

Expected value of determinant of simple infinite random matrix

Show that $(\sum_{k=1}^{n}x_{k}\cos{k})^2+(\sum_{k=1}^{n}x_{k}\sin{k})^2\le (2+\frac{n}{4})\sum_{k=1}^{n}x^2_{k}$

Prove $\int_{0}^{\infty} \cos(\omega x) \exp(-x^{\alpha}) \, {\rm d} x \ge {\alpha^2 \sqrt{\pi} \over 8} \exp \left( -\frac{\omega^2}{4} \right)$

Asymptotic expansion of $\sum\limits_{n=1}^{\infty} \frac{x^{2n+1}}{n!{\sqrt{n}} }$

Lower bounds on analytic functions connected to Fox H

A special type of generating function for Fibonacci

Formula for volume of $n$-ball for negative $n$

Asymptotic behavior of sum linked with Lagrange interpolation

Nice proof of inequality $(1-x^p)^{1/p}(1-x^q)^{1/q}\ge (1-x)(1+x^c)^{1/c}$ where $2^{1/c} = p^{1/p} q^{1/q}$?