Two algebraic identities and the unboundedness of a restricted partition function

Abstract

the coefficients Ch are given by the pentagonal number theorem of Euler [2, p. 284]. Ch also has a combinatorial definition as follows. Let P =(bi, . . ., b,) be a partition of h into unequal summands bi, 1 0. Here we obtain two identities which yield an unbounded sequence of values of anh.1 We will show that