Question

Is it 3-D Catalan numbers?

score 834 · Answer 1 · 2015-05-22 12:14:10

834

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Is it 3-D Catalan numbers?

Published on 22 May 2015 - 12:14

score 509 · Answer 2 · 2015-06-04 16:37:38

509

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Prove a combinatorial identity: $ \sum_{n_1+\dots+n_m=n} \prod_{i=1}^m \frac{1}{n_i}\binom{2n_i}{n_i-1}=\frac{m}{n}\binom{2n}{n-m}$

Published on 04 Jun 2015 - 16:37

score 150 · Answer 3 · 2026-03-27 00:04:27

150

Views

Is there an advantage in using continued fractions for Catalan or Fibonacci-Lucas primality tests?

Published on 27 Mar 2026 - 0:04

score 222 · Answer 4 · 2015-06-09 15:52:59

222

Views

Solving recurrence similar to Catalan number recurrence

Published on 09 Jun 2015 - 15:52

score 501 · Answer 5 · 2015-06-28 12:39:38

501

Views

What is the probability of winning a best of $1, 3, 5, \cdots$ to infinity?

Published on 28 Jun 2015 - 12:39

score 102 · Answer 6 · 2015-07-27 04:51:29

102

Views

Isomorphic relation between Catalan representations

Published on 27 Jul 2015 - 4:51

score 249 · Answer 7 · 2015-08-12 03:25:10

249

Views

How is Schroeder's generalized parentheses sequence (A001003) actually used to generated parentheses expressions?

Published on 12 Aug 2015 - 3:25

score 116 · Answer 8 · 2015-09-18 19:12:54

116

Views

The sum of infinite convergent series where every term is a geometric series term multiplied with reciprocal of square root of n

Published on 18 Sep 2015 - 19:12

score 127 · Answer 9 · 2015-09-22 21:08:52

127

Views

Prove $ 2\cdot5\cdot11\cdot19\cdot23\cdot29\cdot31>3^{16} $

Published on 22 Sep 2015 - 21:08

score 81 · Answer 10 · 2015-09-27 13:32:58

81

Views

$\frac{2n\choose n}{n+2}\not\in\mathbb N$ and $n\neq3k+1$ and $n\neq4k+2$

Published on 27 Sep 2015 - 13:32

score 554 · Answer 11 · 2015-09-29 18:55:46

554

Views

Binomial transform of Catalan numbers formula

Published on 29 Sep 2015 - 18:55

score 3.7k · Answer 12 · 2026-03-27 23:13:50

3.7k

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Finding the number of lattice paths

Published on 27 Mar 2026 - 23:13

score 152 · Answer 13 · 2015-10-08 02:22:11

152

Views

Consider the problem of stacking coins in the plane. Prove that the number of coin configurations satisfies the Catalan recurrence

Published on 08 Oct 2015 - 2:22

score 734 · Answer 14 · 2015-10-09 03:41:07

734

Views

Derive Euler's formula for the Catalan numbers

Published on 09 Oct 2015 - 3:41

score 210 · Answer 15 · 2026-02-27 21:14:50

210

Views

Prove that ${\sum _{n=0} \binom{2n}{n} x^n} = \frac{1}{\sqrt{1-4x}}$

Published on 27 Feb 2026 - 21:14

List Question

Is it 3-D Catalan numbers?

Prove a combinatorial identity: $ \sum_{n_1+\dots+n_m=n} \prod_{i=1}^m \frac{1}{n_i}\binom{2n_i}{n_i-1}=\frac{m}{n}\binom{2n}{n-m}$

Is there an advantage in using continued fractions for Catalan or Fibonacci-Lucas primality tests?

Solving recurrence similar to Catalan number recurrence

What is the probability of winning a best of $1, 3, 5, \cdots$ to infinity?

Isomorphic relation between Catalan representations

How is Schroeder's generalized parentheses sequence (A001003) actually used to generated parentheses expressions?

The sum of infinite convergent series where every term is a geometric series term multiplied with reciprocal of square root of n

Prove $ 2\cdot5\cdot11\cdot19\cdot23\cdot29\cdot31>3^{16} $

$\frac{2n\choose n}{n+2}\not\in\mathbb N$ and $n\neq3k+1$ and $n\neq4k+2$

Binomial transform of Catalan numbers formula

Finding the number of lattice paths

Consider the problem of stacking coins in the plane. Prove that the number of coin configurations satisfies the Catalan recurrence

Derive Euler's formula for the Catalan numbers

Prove that ${\sum _{n=0} \binom{2n}{n} x^n} = \frac{1}{\sqrt{1-4x}}$

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