Problem Statement

Catalan numbers are a sequence of numbers which can be defined directly: Or recursively: Or alternatively (also recursive):

Implement at least one of these algorithms and print out the first 15 Catalan numbers with each. Memoization   is not required, but may be worth the effort when using the second method above.

Let's start with the solution:

procedure main()
every writes(catalan(0 to 14)," ")
end

procedure catalan(n) # return catalan(n) or fail
static M
initial M := table()
n=0 & return 1

if n > 0 then 
   return (n = 1) | \M[n] | ( M[n] := (2*(2*n-1)*catalan(n-1))/(n+1))
end