New posts in binomial-coefficients

Fitting a closed curve on the roots of ${x \choose k}-c$

calculus complex-analysis binomial-coefficients roots curves

An identity on binomial coefficients without using explicit formulas

combinatorics binomial-coefficients

Assume $\alpha, \beta \in \Bbb C,$ such that $\alpha^m = \beta^n = 1$ show that $(\alpha+\beta)^{mn}\in \Bbb R$

calculus complex-analysis algebra-precalculus complex-numbers binomial-coefficients

Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$

combinatorics discrete-mathematics binomial-coefficients combinatorial-proofs

Why General Leibniz rule and Newton's Binomial are so similar?

combinatorics derivatives induction binomial-coefficients intuition

Polynomial in $\mathbb{Q}[x]$ sending integers to integers?

combinatorics polynomials binomial-coefficients

How this operation is called?

combinatorics binomial-coefficients convolution

Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$

summation binomial-coefficients inclusion-exclusion harmonic-numbers coupon-collector

Why does Pascal's Triangle (mod 2) encode the Fermat primes?

combinatorics binomial-coefficients

Simplify a combinatorial sum [duplicate]

combinatorics algebra-precalculus summation binomial-coefficients

Summation of series involving binomial coefficients and polynomial of degree at most n-1

combinatorics polynomials summation binomial-coefficients

Variation on Vandermonde's identity

probability binomial-coefficients random-walk

Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$ [duplicate]

combinatorics summation permutations binomial-coefficients combinatorial-proofs

Is it true that $\lim_{m\to\infty} \sum_{k=0}^{\frac{m-1}{2}} {m\choose{k}}(a^{k+1}(1-a)^{m-k}+a^k(1-a)^{m-k+1})=\min(a,1-a)$?

limits binomial-coefficients binomial-theorem

are there known cases where $\binom{n}{k}$ is a perfect prime power?

combinatorics number-theory prime-numbers binomial-coefficients

Prove a matrix of binomial coefficients over $\mathbb{F}_p$ satisfies $A^3 = I$.

combinatorics binomial-coefficients

Inequality with Sum of Binomial Coefficients

inequality asymptotics binomial-coefficients

A binomial identity

combinatorics sequences-and-series binomial-coefficients

Intuition behind sums of sums of whole numbers

combinatorics summation binomial-coefficients recreational-mathematics intuition

Show that $ \sum_{r=1}^{n-1}\binom{n-2}{r-1}r^{r-1}(n-r)^{n-r-2}= n^{n-2} $

combinatorics summation binomial-coefficients