All Binomial and Summation Identities

This group gathers theorems that state exact formulas for sums and for the expansion of powers, the elementary identities that enumerative combinatorics relies on. It covers Nicomachus's theorem, the identity that the sum of the first n cubes is the square of the nth triangular number, together with expansion identities for powers of sums such as Abel's binomial theorem and the multinomial theorem. Results that count objects with a prescribed structure, such as restricted permutations or graphs of a given kind, belong with Enumerative, Additive and Algebraic Combinatorics.