Inequalities involving the generating function for the number of   partitions into odd parts
  Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of partitions into odd parts and the generating function for the number of odd divisors. 
Cristina Ballantine and Mircea Merca
math.NT math.CO