Catalan numbers

Catalan number formula

For a positiver integer n, the Catalan number is given by the formula:

\(C_n =\dfrac {1} {n+1}\dbinom {2n} {n} =\dfrac {(2n)!} {(n+1)!\, n!}\)

where \(\dbinom {2n} {n}\) is a binomial coefficient.

The first 30 Catalan numbers

C₀ = 1
C₁ = 1
C₂ = 2
C₃ = 5
C₄ = 14
C₅ = 42
C₆ = 132
C₇ = 429
C₈ = 1430
C₉ = 4862
C₁₀ = 16796
C₁₁ = 58786
C₁₂ = 208012
C₁₃ = 742900
C₁₄ = 2674440
C₁₅= 9694845
C₁₆ = 35357670
C₁₇ = 129644790
C₁₈ = 477638700
C₁₉ = 1767263190
C₂₀ = 6564120420
C₂₁ = 24466267020
C₂₂ = 91482563640
C₂₃ = 343059613650
C₂₄ = 1289904147324
C₂₅ = 4861946401452
C₂₆ = 18367353072152
C₂₇ = 69533550916004
C₂₈ = 263747951750360
C₂₉ = 1002242216651368

See also

Binomial coefficient
Permutation