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 thatsmaths.com
The Spine of Pascal's Triangle - ThatsMaths
| | ckrao.wordpress.com
An identity involving the product of reciprocals | Chaitanya's Random Pages
1.8 parsecs away

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| | In this post I would like to prove the following identity, motivated by this tweet. $latex \displaystyle n! \prod_{k=0}^n \frac{1}{x+k} = \frac{1}{x\binom{x+n}{n}} = \sum_{k=0}^n \frac{(-1)^k \binom{n}{k}}{x+k}$ The first of these equalities is straightforward by the definition of binomial coefficients. To prove the second, we make use of partial fractions. We write the expansion $latex \displaystyle...
| | planetmath.org
central binomial coefficient
3.4 parsecs away

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| | [AI summary] This post defines the central binomial coefficient, provides alternative definitions and formulae, and outlines key properties and number theory theorems related to them.
| | cgad.ski
The Central Binomial Coefficient and Laplace's Method
2.1 parsecs away

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| | [AI summary] This article explores the asymptotic growth of the central binomial coefficient using Laplace's method to analyze random walks on integer lattices.
| | kpknudson.com
There Is An Infinite Amount of Hope, Just Not For Us - Kevin Knudson
19.9 parsecs away

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| [AI summary] A mathematician connects Franz Kafka's theme of 'non-arrival' and infinite paradoxes to Georg Cantor's work on different levels of transfinite infinity and the diagonalization argument.