List questions from catalan-numbers

Published on 16 Feb 2023 - 15:22

46

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Dyck paths without centered tunnels

Published on 18 Feb 2023 - 11:34

137

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How to evaluate $\sum_{i=0}^n i^2 C_{i-1} C_{n-i-2}$?

Published on 16 Mar 2023 - 6:26

98

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Catalan interpretation

Published on 16 Mar 2023 - 7:24

63

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Equivalent classes in monotonic lattice paths and Catalan numbers

Published on 18 Mar 2023 - 12:58

236

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Finding the Formula for the Catalan Numbers and Motzkin Numbers

Published on 21 Mar 2023 - 15:32

37

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Balanced binary sequence with odd length.

Published on 17 Apr 2023 - 8:23

133

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A curious identity for powers of the generating function of the Catalan numbers.

Published on 24 Apr 2023 - 16:20

52

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Formal Power Series for Recursion where Successor is Linear Combination of all Predecessors

Published on 05 May 2023 - 17:07

73

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Catalan number's combinatoric proof

Published on 16 May 2023 - 16:56

74

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Geometrical/Combinatorial interpretation of $ \pi = \frac{27}{4 \sqrt 3} \sum_2^∞ \frac{1}{C(k)} $

Published on 16 Jun 2023 - 7:36

26

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Non-Negative Partial Sums and Double Factorial

Published on 01 Jul 2023 - 14:16

101

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Bijection between the set of coin tosses with an equal number of $H$'s and $T$'s and the set where $H$'s and $T$'s are never equal

Published on 06 Aug 2023 - 13:29

192

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Binary string such that always at least as many 0s as 1s

Published on 19 Aug 2023 - 17:35

481

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Finding a closed form for the series $\sum_{n=0}^{\infty}\frac{\binom{2n}{n}^3}{64^n(n+1)^k}$ for $k=1,2,3,4$

Published on 20 Aug 2023 - 11:20

List Question

Left factors $L$ of Dyck paths such that $L$ has $n-1$ up steps

Dyck paths without centered tunnels

How to evaluate $\sum_{i=0}^n i^2 C_{i-1} C_{n-i-2}$?

Catalan interpretation

Equivalent classes in monotonic lattice paths and Catalan numbers

Finding the Formula for the Catalan Numbers and Motzkin Numbers

Balanced binary sequence with odd length.

A curious identity for powers of the generating function of the Catalan numbers.

Formal Power Series for Recursion where Successor is Linear Combination of all Predecessors

Catalan number's combinatoric proof

Geometrical/Combinatorial interpretation of $ \pi = \frac{27}{4 \sqrt 3} \sum_2^∞ \frac{1}{C(k)} $

Non-Negative Partial Sums and Double Factorial

Bijection between the set of coin tosses with an equal number of $H$'s and $T$'s and the set where $H$'s and $T$'s are never equal

Binary string such that always at least as many 0s as 1s

Finding a closed form for the series $\sum_{n=0}^{\infty}\frac{\binom{2n}{n}^3}{64^n(n+1)^k}$ for $k=1,2,3,4$

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