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Catalan numbers

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1: 26.5 Lattice Paths: Catalan Numbers
C ( n ) is the Catalan number. …
Table 26.5.1: Catalan numbers.
n C ( n ) n C ( n ) n C ( n )
26.5.3 C ( n + 1 ) = k = 0 n C ( k ) C ( n k ) ,
2: 26.6 Other Lattice Path Numbers
§26.6(iv) Identities
26.6.12 C ( n ) = k = 1 n N ( n , k ) ,
26.6.13 M ( n ) = k = 0 n ( 1 ) k ( n k ) C ( n + 1 k ) ,
26.6.14 C ( n ) = k = 0 2 n ( 1 ) k ( 2 n k ) M ( 2 n k ) .
3: 26.1 Special Notation
( m n ) binomial coefficient.
C ( n ) Catalan number.
4: 25.11 Hurwitz Zeta Function
where H n are the harmonic numbers:
25.11.33 H n = k = 1 n k 1 .
25.11.39 k = 2 k 2 k ζ ( k + 1 , 3 4 ) = 8 G ,
where G is Catalan’s constant:
25.11.40 G n = 0 ( 1 ) n ( 2 n + 1 ) 2 = 0.91596 55941 772 .