This function is graphically represented by a slope-1 line through the point (0,1) "zero comma one".
The nth Catalan number is given by 2n choose n divided by this function of n, and the coefficients of this function to the kth power are found in the kth row of Pascal's Triangle. To prove an argument via induction, one proves that if the statement is true for a value n, it is also true for this function of n. The remainder when a polynomial P is divided by this function is (*) P(-1) ["P of negative one"], and if there are n holes and at least this many pigeons, two of them will be in the same hole. This function is graphically represented by a slope-1 line through the point (0,1) "zero comma one". For ten points, name this function, which, when applied to an integer, yields the next higher integer.
The nth Catalan number is given by 2n choose n divided by this function of n, and the coefficients of this function to the kth power are found in the kth row of Pascal's Triangle.
n+1 (“n plus one”, accept also stuff like “adding one” or anything that implies the number coming out is one bigger than the one going in, or anything with a different variable than n like x+1) &lt;MS&gt;