@inbook{10.4169/j.ctt13x0ng0.19,
URL = {http://www.jstor.org/stable/10.4169/j.ctt13x0ng0.19},
abstract = {The well known Catalan numbersCnare 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 inScientific 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 numbersCnare often defined by the explicit formula${{C}_{n}}=\frac{1}{n+1}\left( \begin{matrix} 2n\\ n\\ \end{matrix} \right)$, wheren≥ 0},
author = {Thomas Koshy and Zhenguang Gao},
booktitle = {Martin Gardner in the Twenty-First Century},
edition = {1},
pages = {119--124},
publisher = {Mathematical Association of America},
title = {Convergence of a Catalan Series},
year = {2012}
}