The q-Lah numbers and the nth q-derivative of exp_q(1/n)

Jacob Katriel
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 45–47
Full paper (PDF, 145 Kb)

Details

Authors and affiliations

Jacob Katriel
Department of Chemistry, Technion – Israel Institute of Technology
Haifa 32000, Israel

Abstract

A recently reported nice and surprising property of the Lah numbers is shown to hold for q-Lah numbers as well, i.e., they can be obtained by taking successive q-derivatives of exp_q(1/n), where exp_q(x) is the q-exponential.

Keywords

• q-Lah numbers
• q-exponential

AMS Classification

• 11B65
• 11B73

References

1. Daboul, S., Mangaldan, J., Spivey, M. Z. & Taylor, P. J. (2013) The Lah numbers and the n‘th derivative of e ^1/x . Math. Magazine, 86, 39–47.
2. Garsia, A. M. & Remmel, J. (1980) A combinatorial interpretation of q-derangement and q-Laguerre numbers, Europ. J. Combinatorics, 1, 47–59.
3. Lindsay, J., Mansour, T. & Shattuck, M. (2011) A new combinatorial interpretation of a q-analogue of the Lah numbers, J. Combinatorics, 2, 245–264.
4. Wagner, C. G. (1996) Generalized Stirling and Lah numbers, Discrete Math., 160, 199–218.