# Tagged Questions

2answers
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### Sums of central binomial coefficients

Are there closed forms for $$\sum^n_{i=0} \binom{2i}{i}$$ and $$\sum^n_{i=0} \binom{2i}{i}^2$$? Also, how can these sums be approximated?
0answers
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### Good upper bound on a binomial sum

What is a good upper bound on the following binomial sum: $$\sum_{i,j< \frac{m}{n}} {m \choose i}{m-i \choose j} z^{i+j}$$ where $z = \frac{1}{n-2}$?
1answer
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1answer
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0answers
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### Calculation of sum

I am wondering if it is possible to calculate or approximate the following sum $$\sum_{k=0}^l\frac{(l-2k)^p(2l+k(k-1))l^{k-1}}{(k+3)(k+2)}$$here $p \geq 2$. Thank you.
2answers
389 views

### Elementary bound of binomial coefficient

I'm working my way through an ErdÅ‘s paper from the sixties and some of the elementary bounds he claims seem to be just beyond my reach. The expression looks horrendous but maybe there is a clever ...
0answers
281 views

### Calculation of a 'double' sum

Let $n \in N$ and $q\geq 2$. I am trying to calculate the following sum: $$\sum_{i=0}^{\sqrt n/2}\sum_{j= i \sqrt n }^{(i+1)\sqrt n}\frac{(-1)^q2^q(\frac{n}{2}-j)^q}{(n-j)!j!}$$ Any help will be ...
1answer
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2answers
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### Approximating the logarithm of the binomial coefficient

We know that by using Stirling approximation: $\log n! \approx n \log n$ So how to approximate $\log {m \choose n}$?
3answers
3k views

### How to simplify or calculate a formula with very big factorials

I'm facing a practical problem where I've calculated a formula that, with the help of some programming, can bring me to my final answer. However, the numbers involved are so big that it takes ages to ...