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Results tagged with catalan-numbers
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user 48831
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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votes
Accepted
A polynomial identity related to Catalan numbers
These assertions can be proved using (formal) generating functions.
Using that for $j\geq 0, k\geq 1$
\begin{align*}
\sum_{n\geq 0} {n-j+kj \choose kj} t^n &=\frac{t^j}{(1-t)^{kj+1} }\;\;\mbox{ …
- 3,255