This theorem gives rise to numbers that can count the ways of choosing k elements from a set of n elements, and those coefficients are equal to the values in a row of Pascal's Triangle.
When divided by "n plus 1," the nth central number derived from this statement gives the nth Catalan number. This statement was first proven for complex numbers by Abel, though that generalization had been stated by Newton. This theorem gives rise to numbers that can count the ways of choosing k elements from a set of n elements, and those coefficients are equal to the values in a row of Pascal's Triangle. For 10 points, name this theorem which gives the expansion of "the quantity x plus y, to the nth power."
When divided by "n plus 1," the nth central number derived from this statement gives the nth Catalan number.
{Binomial} Theorem [or reasonable equivalents of Theorem like {Binomial Identity}; or {Binomial Coefficient}]