单词 | Catalan Number | ||||||||||||||||||||||||||||||||||||||||||
释义 | Catalan NumberThe Catalan numbers are an Integer Sequence ![]() The first few Catalan numbers are 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, ... (Sloane's A000108). The only OddCatalan numbers are those of the form The Catalan numbers turn up in many other related types of problems. For instance, the Catalan number ![]() the number of states possible in an An explicit formula for
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so
Segner's Recurrence Formula, given by Segner in 1758, gives the solution to Euler's Polygon DivisionProblem
![]() ![]() The Generating Function for the Catalan numbers is given by
A generalization of the Catalan numbers is defined by
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