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of counting seating arrangements in which men and women alternate and are not seated next to their spouses.
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282:" giving an overwhelming plenitude of different definitions for the Catalan numbers). For
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520:{\displaystyle C(t)=\sum _{n\geq 0}C_{n}t^{n}={{1-{\sqrt {1-4t}}} \over {2t}}}
644:{\displaystyle {t \over {1-2t}}C\left({t^{2} \over (1-2t)^{2}}\right)=C(t)-1}
404:{\displaystyle C_{n+1}=\sum _{k\,\leq \,n/2}2^{n-2k}{n \choose 2k}C_{k}.\,}
264:{\displaystyle C_{k}={1 \over {k+1}}{{2k} \choose {k}},\quad k\geq 0}
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it can be proved by algebraic manipulations of generating
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280:Exercises on Catalan and Related Numbers
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51:adding citations to reliable sources
699:. You can help Knowledge (XXG) by
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416:generating function
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45:Please help
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751:1885 births
107:August 2011
740:Categories
414:Using the
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451:≥
444:∑
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