MathOverflow

Let
$f(n,m)$ be a function such that $$ f(n,m) = mf(n-1,m) + 1, \\ f(0,m) = 1. $$
$T(n,m)$ be a coefficients such that $$ T(n,m) = n! \sum\limits_{k=1}^{n} \frac{m^{k-1} n^{n-k-1}}{(n-k)!}. $$See related sequences A001865 ($m=1$) and A133297 ($m=-1$).

Let $X,Y,Z$ independent Gaussian r.v.'s with mean=variance. Let's denote these mean/variance parameters by $g_X,g_Y,g_Z>0$ respectively.I am interested in the distribution of $T_1:=\tanh X$ and $T_2:=\tanh Y\tanh Z$.In particular I wonder if for...

Let�be a family of subsets of[�]such that for any two distinct sets�,�∈�, we have
∣�∩�∣≤�.For fixed�, what is known about the maximum possible size of such a family as�→∞?
Are there sharp asymptotic bounds or explicit constructions beyond the classical Erdős–Ko–Rado type results?...

I'm currently dealing with a Gibbs sampler of the multivariate generalized inverse Gaussian distribution (MGIG). In order to check the correctness of the sampler, I'd like to know the expected value of this distribution. I read a couple of papers involving...