import integers.choose
import util.TextTable

def
  catalan( n ) = choose( 2n, n )/(n + 1)

  catalan2( n ) = product( (n + k)/k | k <- 2..n )

  catalan3( 0 ) = 1
  catalan3( n ) = 2*(2n - 1)/(n + 1)*catalan3( n - 1 )

t = TextTable()
t.header( 'n', 'definition', 'product', 'recursive' )
t.line()

for i <- 1..4
  t.rightAlignment( i )

for i <- 0..15
  t.row( i, catalan(i), catalan2(i), catalan3(i) )

println( t )