Journal of Integer Sequences, Vol. 26 (2023), Article 23.9.8

Polynomial Identities Involving Binomial Coefficients and Double and Rising Factorials via Probabilistic Interpretations

Paweł J. Szabłowski*
Department of Mathematics and Information Sciences
Warsaw University of Technology
ul. Koszykowa 75
00-662 Warsaw


We formulate several polynomial identities. One side of these identities has a nice simple form, whereas the other has the form of a polynomial whose coefficients contain binomial coefficients, double factorials, or rising factorials. The origins and the proofs of these identities are probabilistic. However, their form suggests universal applications in simplifying expressions. Many useful simplifying formulae are presented in the sequel.

* Retired.

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(Concerned with sequences A000032 A000045 A001147 A007318 A221954.)

Received July 7 2023; revised versions received November 7 2023, November 13 2023. Published in Journal of Integer Sequences, January 3 2024.

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