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Results tagged with catalan-numbers
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user 11259
The Catalan numbers form the sequence of numbers starting 1,1,2,5,14,42,... with explicit formula $\frac{1}{n+1}\binom{2n}{n}$. It counts many combinatorial objects like planar binary trees, triangulations, noncrossing partitions, Dyck paths, etc. See https://oeis.org/A000108
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Probability of a Random Walk crossing a straight line
Let $(S_n)_{n=1}^{\infty}$ be a standard random walk with $S_n = \sum_{i=1}^n X_i$ and $\mathbb{P}(X_i = \pm 1) = \frac{1}{2}$. Let $\alpha \in \mathbb{R}$ be some constant. I would like to know the v …
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