# Tagged Questions

40 views

### Binomial Congruence (mod 5) Identity

I've got a (hard?) Putnam-style problem that I've been given to look at . . . I've never worked any problem even vaguely like this, but my director thinks I should be able to do it. I doubt it (100% ...
44 views

156 views

### Closed form of a sum of binomial coefficients?

I have the following function: $T_n(d)=\sum\limits_{k=\frac{n-d}{2}}^{\lceil \frac{n}{2} \rceil}{k\choose \frac{n-d}{2}}$ ${n \choose 2k}$, where $n,d\in \mathbb{N}^0$, and $n,d$ have the same ...
70 views

### Conjecture for product of binomial coefficient

Is it true that for any $n, k\in\mathbb N$ $$\frac{(kn)!}{k!(n!)^k} = \prod_{l=1}^k {{ln-1}\choose{n-1}} \quad?$$ I tested it for some small $k$ and $n$, but I don't know how to prove that it is true ...
101 views

### Given the sequence $3, 4, 11, 16, 42\ldots$ how can I derive a general formula for it?

Given a sequence $3, 4, 11, 16, 42\ldots$ how can I derive a general formula for this sequence? Is there any optimised approach? My approach: the given series is equal to summation of $\binom{n}{k}$ ...
189 views