Catalan numbers

This tool calculates the n-th Catalan number.



Catalan number formula

For a positiver integer n, the Catalan number is calculated from the binomial coefficient as following,

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

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