do  -- print some catalan numbers
    local function printCatalan( n : number, cn : number )
        print( string.format( "%3d: %d", n, cn ) )
    end
    local Cprev = 1 -- C0
    printCatalan( 0, Cprev )
    for n = 1, 15 do
        Cprev = math.round( ( ( ( 4 * n ) - 2 ) / ( n + 1 ) ) * Cprev )
        printCatalan( n, Cprev )
    end
end