Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.7

A Generating Function for Numbers of Insets

Milan Janjić
Department of Mathematics and Informatics
University of Banja Luka
Banja Luka, 78000
Republic of Srpska, Bosnia and Herzegovina


In a previous paper, we defined the notion of inset. In this paper, we first derive a generating function for the number of insets in terms of one of its parameters. Using this function, we connect insets with some important classes of integers.

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.

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(Concerned with sequences A000041 A008302 A010815.)

Received February 23 2014; revised version received July 13 2014; September 4 2014. Published in Journal of Integer Sequences, September 4 2014.

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