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Results tagged with binomial-coefficients
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user 119995
For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.
1
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0
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Upper bound $\sum_{i=1}^m \sum_{j=1}^n p_{i,j}(1-p_{i,j})$
Let
$$p_{i,j} = \frac{\sum_{l=i}^{i+j-1} {l-1 \choose i-1} {m+n-l \choose m-i}}{{m+n \choose n}}$$
I am interested in approximating/upper bounding the sum
$$ \sum_{i=1}^m \sum_{j=1}^n p_{i,j}(1-p_{i,j …
- 662
3
votes
How to find the coefficient of $x^k$ in the expression $\prod_{p=1}^n (x^p+1)^p$?
Caveat: OP asked me in the comment section how he can calculate the coefficient explicitly. This answer is mainly algorithmic (dynamic programming) and straight forward with FFT/convolutions/dynamic p …
- 662