List questions from catalan-numbers

Published on 13 Oct 2015 - 4:34

897

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Prove the following two statements about the Catalan numbers $C_n$

Published on 14 Oct 2015 - 19:13

835

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Let ${a_n}$ be a sequence of real numbers. The backwards differences of this sequence are defined recursively:

Published on 06 Mar 2026 - 21:21

1.2k

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Number of pathsin a grid with restrictions

Published on 28 Feb 2026 - 3:01

958

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Recurrence relation of Catalan Numbers.

Published on 10 Nov 2015 - 11:29

890

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Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

Published on 17 Nov 2015 - 11:49

284

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A series related to Catalan numbers

Published on 15 Mar 2026 - 23:00

10k

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Number of ways to pair off $2n$ points such that no chords intersect

Published on 26 Nov 2015 - 19:34

378

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Confused about Catalan number equation

Published on 30 Nov 2015 - 19:15

544

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Is there a unique definition of Catalan numbers?

Published on 01 Dec 2015 - 21:14

170

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Groups and Catalan Numbers

Published on 01 Dec 2015 - 21:40

9.1k

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Prove the generating function for the Catalan number sequence is $f(x) = \frac{1 -\sqrt{1-4x}}{2x}$

Published on 01 Dec 2015 - 22:03

582

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Catalan numbers generating function

Published on 02 Dec 2015 - 6:44

354

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Proving that the Catalan numbers are integers .

Published on 04 Dec 2015 - 3:26

535

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How to prove $\sum_{s=0}^{m}{2s\choose s}{s\choose m-s}\frac{(-1)^s}{s+1}=(-1)^m$?

Published on 04 Dec 2015 - 11:32

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321-avoiding permutations and RSK

Prove the following two statements about the Catalan numbers $C_n$

Let ${a_n}$ be a sequence of real numbers. The backwards differences of this sequence are defined recursively:

Number of pathsin a grid with restrictions

Recurrence relation of Catalan Numbers.

Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

A series related to Catalan numbers

Number of ways to pair off $2n$ points such that no chords intersect

Confused about Catalan number equation

Is there a unique definition of Catalan numbers?

Groups and Catalan Numbers

Prove the generating function for the Catalan number sequence is $f(x) = \frac{1 -\sqrt{1-4x}}{2x}$

Catalan numbers generating function

Proving that the Catalan numbers are integers .

How to prove $\sum_{s=0}^{m}{2s\choose s}{s\choose m-s}\frac{(-1)^s}{s+1}=(-1)^m$?

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