Question

Solve Summation of Catalan Convolution?

score 102 · Answer 1 · 2022-01-29 17:19:40

102

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Solve Summation of Catalan Convolution?

Published on 29 Jan 2022 - 17:19

score 628 · Answer 2 · 2026-03-30 00:21:25

628

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Calculating the Moments of the Marchenko-Pastur Distribution

Published on 30 Mar 2026 - 0:21

score 108 · Answer 3 · 2026-03-27 13:46:24

108

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Generalized Catalan number satisfying recursive definition

Published on 27 Mar 2026 - 13:46

score 108 · Answer 4 · 2022-03-25 15:09:10

108

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How to prove number of permutations obtained by a deque is C(2(n-1),n-1)?

Published on 25 Mar 2022 - 15:09

score 93 · Answer 5 · 2022-03-26 03:41:59

93

Views

Infinite Catalan Sum involving polynomials

Published on 26 Mar 2022 - 3:41

score 42 · Answer 6 · 2022-04-11 15:29:58

42

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The intuitive correspondence between the multiplication schemes (or triangularizations) and -1s 1s sequences.

Published on 11 Apr 2022 - 15:29

score 41 · Answer 7 · 2022-04-23 12:44:06

41

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How do we handle the factorials in the binomials/choice numbers?

Published on 23 Apr 2022 - 12:44

score 134 · Answer 8 · 2022-04-23 12:57:49

134

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Why are the catalan numbers giving the unique/correct patterns from all the combinations?

Published on 23 Apr 2022 - 12:57

score 208 · Answer 9 · 2022-04-26 11:04:55

208

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Counting all possible pairs of parenthesis

Published on 26 Apr 2022 - 11:04

score 152 · Answer 10 · 2022-04-26 19:42:08

152

Views

How is the diagonal constraint in lattice path needed for the Catalan proofs?

Published on 26 Apr 2022 - 19:42

score 770 · Answer 11 · 2022-05-18 20:48:20

770

Views

Intuitive Explanation for Number of Dyck Paths Never Going Above Diagonal of a Rectangle

Published on 18 May 2022 - 20:48

score 75 · Answer 12 · 2022-06-03 15:34:07

75

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Analytic formula for $E(\rho):=\sum_{m=0}^\infty \mu_m(\rho)/m!$, with $\mu_m(\rho) := \sum_{k=0}^{m-1}\dfrac{\rho^k}{k+1}{m \choose k}{m-1\choose k}$

Published on 03 Jun 2022 - 15:34

score 363 · Answer 13 · 2022-06-13 03:29:47

363

Views

Conjecture: $\frac1\pi=\sum_{n=0}^\infty\left((n+1)\frac{C_n^3}{2^{6n}}\sum_{k=0}^n(-1)^k{n\choose k}{\frac{(n-k)(k-1)}{(2k-1)(2k+1)}}\right)$

Published on 13 Jun 2022 - 3:29

score 383 · Answer 14 · 2022-07-16 19:53:14

383

Views

Factors of central binomial coefficient

Published on 16 Jul 2022 - 19:53

score 148 · Answer 15 · 2022-07-31 00:23:45

148

Views

Proof of equating coefficients validity in Catalan number formula derivation?

Published on 31 Jul 2022 - 0:23

List Question

Solve Summation of Catalan Convolution?

Calculating the Moments of the Marchenko-Pastur Distribution

Generalized Catalan number satisfying recursive definition

How to prove number of permutations obtained by a deque is C(2(n-1),n-1)?

Infinite Catalan Sum involving polynomials

The intuitive correspondence between the multiplication schemes (or triangularizations) and -1s 1s sequences.

How do we handle the factorials in the binomials/choice numbers?

Why are the catalan numbers giving the unique/correct patterns from all the combinations?

Counting all possible pairs of parenthesis

How is the diagonal constraint in lattice path needed for the Catalan proofs?

Intuitive Explanation for Number of Dyck Paths Never Going Above Diagonal of a Rectangle

Analytic formula for $E(\rho):=\sum_{m=0}^\infty \mu_m(\rho)/m!$, with $\mu_m(\rho) := \sum_{k=0}^{m-1}\dfrac{\rho^k}{k+1}{m \choose k}{m-1\choose k}$

Conjecture: $\frac1\pi=\sum_{n=0}^\infty\left((n+1)\frac{C_n^3}{2^{6n}}\sum_{k=0}^n(-1)^k{n\choose k}{\frac{(n-k)(k-1)}{(2k-1)(2k+1)}}\right)$

Factors of central binomial coefficient

Proof of equating coefficients validity in Catalan number formula derivation?

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