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 Mar 24 comment High order central moments of a symmetric binomial variable Since I'm interested in $M^r$, this gives an estimate tight up to a factor exponential in $r$. Will update if I find anything better. Again, thank you very much. Mar 24 comment High order central moments of a symmetric binomial variable Thanks! This reference is pretty much what I was looking for. Mar 24 accepted High order central moments of a symmetric binomial variable Mar 18 comment High order central moments of a symmetric binomial variable @BrendanMcKay, I'll try your suggestion and post an answer if I succeed. Thanks! Mar 18 revised High order central moments of a symmetric binomial variable edited tags Mar 18 comment High order central moments of a symmetric binomial variable @usul, you've actually given my motivation for asking this question. I started by looking for the asymptotics of the number of sequences of vectors in $\{1\ldots n\}^r$ in which each element appears an even number of times. :-) Mar 17 awarded Editor Mar 17 comment High order central moments of a symmetric binomial variable John, can you tell me what special functions are you referring to? Thanks! Mar 17 revised High order central moments of a symmetric binomial variable deleted 49 characters in body Mar 17 comment High order central moments of a symmetric binomial variable Joris, I mean asymptotic behaviour as $n\to \infty$. I considered the normal approximation, but from the central limit theorem (at least the standard version), I'm not sure how to bound the error here. Mar 17 comment High order central moments of a symmetric binomial variable Thank you. Indeed, the binomial formula yields an exact expression, but what I'm looking for is the asymptotic growth of this expression. I will edit the question to reflect this. Mar 17 asked High order central moments of a symmetric binomial variable Mar 18 accepted Probability of a giant component existing in a $G(n,p)$ random graph with $p=\omega(\frac 1n)$ Jan 25 asked Probability of a giant component existing in a $G(n,p)$ random graph with $p=\omega(\frac 1n)$ Sep 10 comment An upper bound for the growth of a Galton-Watson tree with binomial offspring distribution Will look. Thanks! Sep 6 comment An upper bound for the growth of a Galton-Watson tree with binomial offspring distribution I am interested in the case where $np>1$. Specifically, $p=\Theta(\frac{\log n}{n})$. Sep 5 awarded Informed Sep 5 asked An upper bound for the growth of a Galton-Watson tree with binomial offspring distribution Apr 12 awarded Supporter Feb 2 awarded Student