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CatalanNumber

CatalanNumber[n]
gives the n^(th) Catalan number .
MORE INFORMATION
  • Catalan numbers are integers, and appear in various tree enumeration problems.
EXAMPLESCLOSE ALL
Basic Examples   (1)
The first 10 Catalan numbers:
The first 10 Catalan numbers:
In[1]:=
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Out[1]=
Scope   (3)
Evaluate for large arguments:
CatalanNumber threads element-wise over lists:
TraditionalForm typesetting:
Applications   (1)
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:
Properties & Relations   (1)
The generating function for Catalan numbers:
Neat Examples   (2)
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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