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for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
2
votes
Asymptotic behaviour of sequence
For sums like this, usually one term dominates. Taking $p(n)=n^d$ to play with, consider
when $\binom{(n-k)^d}{k} \lt \binom{(n-k-1)^d}{k+1}$ stops holding. This is not far from
when $(k+1) \lt (\fr …
1
vote
Accepted
Finding the min of a sequence related with factorials
Lemma: Let $n,a$, be positive integers with $r = n \bmod a$, the remainder after
dividing $n$ by $a$. Using Iverson notation [statement] is $1$ if true, $0$ otherwise,
$\lfloor 2n/a \rfloor = 2\lfloo …