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TY - CHAP
TI - Convergence of a Catalan Series
AU - Koshy, Thomas
AU - Zhenguang Gao
A3 - Henle, Michael
A3 - Hopkins, Brian
AB - The well known Catalan numbers*C*_{n}are named after Belgian mathematician Eugene Charles Catalan (1814–1894), who found them in his investigation of well-formed sequences of left and right parentheses. As Martin Gardner (1914–2010) wrote in*Scientific American*[2], they have the propensity to “pop up in numerous and quite unexpected places.” They occur, for example, in the study of triangulations of convex polygons, planted trivalent binary trees, and the moves of a rook on a chessboard [1, 2, 3, 4, 6].

The Catalan numbers*C*_{n}are often defined by the explicit formula${{C}_{n}}=\frac{1}{n+1}\left( \begin{matrix} 2n\\ n\\ \end{matrix} \right)$, where*n*≥ 0

EP - 124
ET - 1
PB - Mathematical Association of America
PY - 2012
SN - null
SP - 119
T2 - Martin Gardner in the Twenty-First Century
UR - http://www.jstor.org/stable/10.4169/j.ctt13x0ng0.19
Y2 - 2020/09/29/
ER -