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CatalanNumber

CatalanNumber[n]
gives the n^(th) Catalan number .
  • Catalan numbers are integers, and appear in various tree enumeration problems.
The first 10 Catalan numbers:
The first 10 Catalan numbers:
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Click for copyable input
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Evaluate for large arguments:
CatalanNumber threads element-wise over lists:
TraditionalForm typesetting:
Compute the number of different ways to parenthesize an expression:
Distribute over lists in AngleBracket:
Use the pattern matcher to repeatedly split the list into two parts in all possible ways:
The number of ways to parenthesize the expression :
Check:
The generating function for Catalan numbers:
The only odd Catalan numbers are those of the form CatalanNumber:
Determinants of Hankel matrices made out of Catalan numbers:
Compare to Fibonacci numbers:
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