Journal of Integer Sequences, Vol. 20 (2017), Article 17.10.4

Identities for Generalized Whitney and Stirling Numbers

Mark Shattuck
Institute for Computational Science
Faculty of Mathematics and Statistics
Ton Duc Thang University
Ho Chi Minh City


In this paper, we prove by algebraic methods two further formulas satisfied by the r-Whitney numbers of the second kind, which have been an object of recent study. We establish a version of one of the formulas for a polynomial generalization of the r-Whitney numbers. As special cases, we obtain apparently new identities for the Stirling numbers of the second kind and the Bell numbers. Moreover, one may obtain analogous formulas for Lah numbers and Stirling numbers of the first kind.

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(Concerned with sequences A000110 A000262 A008275 A008277 A008297.)

Received April 18 2017; revised version received September 27 2017. Published in Journal of Integer Sequences, October 29 2017.

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