|Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.7|
We first prove that the numbers of integer partitions satisfy a system of homogeneous linear equations. Then we derive an explicit formula for the coefficients of the Euler product function in terms of the number of insets. As a consequence, we express the Euler pentagonal number theorem in terms of insets.
Finally, we derive an explicit formula for the entries of the Mahonian triangle.
(Concerned with sequences
Received February 23 2014; revised version received July 13 2014; September 4 2014. Published in Journal of Integer Sequences, September 4 2014.