include "NSLog.incl"

local fn Factorial( n as NSInteger ) as UInt64
  UInt64 sum = 0

  if n = 0 then sum = 1 : exit fn
  sum = n * fn Factorial( n - 1 )
end fn = sum

local fn Catalan1( n as NSInteger ) as UInt64
  UInt64     product = 1, result
  NSUInteger i

  for i = n + 2 to 2 * n
    product = product * i
  next
  result = product / fn Factorial( n )
end fn = result

local fn Catalan2( n as NSInteger ) as UInt64
  UInt64     sum = 0
  NSUInteger i

  if n = 0 then sum = 1 : exit fn
  for i = 0 to n - 1
    sum += fn Catalan2(i) * fn Catalan2( n - 1 - i )
  next
end fn = sum

local fn Catalan3( n as NSInteger ) as UInt64
  UInt64 result

  if n = 0 then result = 1 : exit fn
  result = fn Catalan3( n - 1 ) * 2 * ( 2 * n - 1 ) / ( n + 1 )
end fn = result

NSUInteger i

for i = 0 to 19
  if( i < 16 )
    NSLog( @"%3d.\t\t%7llu\t\t%12llu\t\t%12llu", i, fn Catalan1( i ), fn Catalan2( i ), fn Catalan3( i ) )
  else
    NSLog( @"%3d.\t\t%@\t\t%12llu\t\t%12llu", i, @"[-err-]", fn Catalan2( i ), fn Catalan3( i ) )
  end if
next

HandleEvents