In this paper we define the nth polygonal polynomial P_n(z) = (z-1)(z^2-1)\cdots(z^n-1) and we investigate recurrence relations and exact integral formulae for the coefficients of P_n and for those of the Mahonian polynomials Q_n(z)=(z+1)(z^2+z+1)\cdots(z^{n-1}+\cdots+z+1). We also explore numerical properties of these coefficients, unraveling new meanings for old sequences and generating novel entries to the Online Encyclopedia of Integer Sequences (OEIS). Some open questions are also formulated.



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Andrica, Dorin, Bagdasar, Ovidiu D.