While the Catalan numbers are the number of p-good paths from (n, n) to (0, 0) which do not cross the diagonal line, the super Catalan numbers count the number of lattice paths with diagonal steps from (n, n) to (0, 0) which do not touch the diagonal line x = y. The super Catalan numbers are given by the recurrence relation S(n) = (3(2n - 3) S(n - 1) - (n - 3) S(n - 2))/n (Comtet 1974), with S(1) = S(2) = 1.

bracketing | Catalan number | integer sequence primes | Schröder number

Eugène Charles Catalan