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The generalised Catalan Numbers and Borel's Triangle

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#sequences-and-series #combinatorics #catalan-numbers
180
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combinatorics - how many ways can I add/subtract 1 from 4 40 times and reach zero without dropping below

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#combinatorics #catalan-numbers
71
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Proving an algebraic binomial identity related to Bertrand's ballot theorem

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#combinatorics #proof-writing #catalan-numbers
129
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What is the generating function of $z^3 + 2z^5 + 5z^7 + 14 z^9+\dots$?

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#sequences-and-series #power-series #generating-functions #catalan-numbers
81
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Showing that $\lim_{n \to \infty}\frac{c_n}{4^n} = 0$

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#combinatorics #analysis #catalan-numbers
129
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How many ways to split a convex polygon to squares?

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#combinatorics #generating-functions #catalan-numbers #lagrange-inversion
511
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Is there a closed form for a give infinite sum?

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#sequences-and-series #harmonic-numbers #catalan-numbers
74
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Number of specific functions $f:[2n]\to[2n]$ are Catalan Numbers

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#catalan-numbers
230
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Generating function of a parametrized binomial coefficient

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#combinatorics #power-series #binomial-coefficients #generating-functions #catalan-numbers
36
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Bound on number of Dyck paths that stay below M for M large

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#combinatorics #random-walk #catalan-numbers
101
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All the routes from $(0,0)$ to $(6,6)$ such that no route passes $y = x+2$ - Catalan numbers

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#combinatorics #catalan-numbers
1.2k
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Catalan numbers - algebraic proof of the recurrence relation

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#combinatorics #proof-writing #binomial-coefficients #catalan-numbers
65
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Catalan number but with "bad moves"

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#combinatorics #discrete-mathematics #catalan-numbers
133
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expansion of Catalan number based on combination

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#combinatorics #catalan-numbers
107
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Relations between two applications of Catalan Numbers

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#combinatorics #catalan-numbers

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