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The number of binary trees with $n$ nodes, $p$ left children, $q$ right children ($p+q ...his, and hence the number of binary trees with $k+1$ nodes, is the Catalan number

Named after its inventor, E.Ch. Catalan (1814–1894), the Catalan constant $G$ (which is denoted also by $\lambda$) is defined by which provides a relationship between the Catalan constant $G$ and the Digamma function $\psi ( z )$.

...=1,\ldots,2n$. The number of such sequences is given by the $n$-th Catalan number The first few Catalan numbers are: $C_0=1$, $C_1 = 1$, $C_2 = 2$, $C_3 = 5$, $C_4 = 14$, $C_5 = 4

is a fixed non-zero algebraic number, and the polynomial $ F ( X,1 ) $ ...ight of the solutions, either in the ring of integers of a fixed algebraic number [[Field|field]] $ K $,

depends on the average number, $ m $, of male children per male parent. If $ m \leq 1 $ just before his own death, to E.C. Catalan (1814-1894). It is a testament, prophetic

industry, perfected a number of inventions which won him gold and Catalan refugee. After a few years in Florence and the failure of a

...Meusnier, 1776) and the [[Helicoid|helicoid]] (Meusnier, 1776). In 1842 E. Catalan proved that the helicoid is the unique ruled minimal surface; in 1844 the [ ...holomorphic mappings this problem has a complete solution. There is also a number of results on the intrinsic nature of the metrics of two-dimensional minima

...ge behaviour and, furthermore, the sheer size of the required rule set and number of lexical items has up to now (2000) prevented linguists from providing a ...} { 2 n } \\ { n - 1 } \end{array} \right)$, where $\mathcal{C}_n$ is the number of ways to parenthesize a formula of length $n$ [[#References|[a5]]].