New posts in binomial-coefficients

Inequality between binomial sums

combinatorics inequality binomial-coefficients hypergeometric-function

When $\frac{C(n, k)}{n^{k-1}} > 1$?

combinatorics binomial-coefficients

Asymptotic Behavior of a Sum with Binomial Coefficients

combinatorics asymptotics binomial-coefficients

finding the combinatorial sum [duplicate]

combinatorics binomial-coefficients

Prove that $\exp(\log(\frac{1}{1-x})) = \frac{1}{1-x}$

combinatorics binomial-coefficients power-series generating-functions

Simplifying sum with rising and falling factorials

summation binomial-coefficients factorial

Summation of an Infinite Series: $\sum_{n=1}^\infty \frac{4^{2n}}{n^3 \binom{2n}{n}^2} = 8\pi G-14\zeta(3)$

calculus real-analysis sequences-and-series binomial-coefficients summation

Prove the identity $\binom{2n+1}{0} + \binom{2n+1}{1} + \cdots + \binom{2n+1}{n} = 4^n$

summation binomial-coefficients binomial-theorem

Proving a certain binomial identity with three parameters

combinatorics binomial-coefficients

Combinatorial sum identity for a choose function $\sum\limits_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ [duplicate]

combinatorics discrete-mathematics summation binomial-coefficients

Binomial Coefficient

binomial-coefficients generating-functions inverse-function

Is there a combinatorial way to see the link between the beta and gamma functions?

combinatorics special-functions binomial-coefficients gamma-function

Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$

combinatorics summation binomial-coefficients generating-functions

Simplify binomial sum

summation binomial-coefficients eulerian-numbers

On closed forms for the binomial sum $\sum_{n=1}^\infty \frac{z^n}{n^p\,\binom {2n}n}$ for general $p$?

integration sequences-and-series definite-integrals binomial-coefficients closed-form

Combinatorial identity from squaring the binomial expansion

combinatorics binomial-coefficients binomial-theorem combinatorial-proofs

$\sum_{n=1}^\infty\frac{n}{(2n-1)16^n}\binom{2n}{n}^2\left(\sum_{k=n}^\infty\frac{2^k}{k\binom{2k}{k}}\right)=1-\sqrt2+\log(1+\sqrt2).$

calculus sequences-and-series binomial-coefficients book-recommendation summation-method

Proof of a binomial identity $\sum_{k=0}^n {n \choose k}^{\!2} = {2n \choose n}.$

combinatorics summation proof-writing binomial-coefficients taylor-expansion

Calculate the binomial $(1-x)^{-(n+1)}$

summation binomial-coefficients

A Binomial Coefficient Sum: $\sum_{m = 0}^{n} (-1)^{n-m} \binom{n}{m} \binom{m-1}{l}$

combinatorics summation binomial-coefficients