Some properties of modified Lah numbers

A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 7, 2001, Number 4, Pages 125–131
Full paper (PDF, 180 Kb)

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Authors and affiliations

A. G. Shannon
Warrane College, The University of New South Wales, 1465, &
KvB Institute of Technology, North Sydney, 2060, Australia

Abstract

A modification of Lah numbers is suggested in this paper by defining them in relation to the rising factorial coefficients instead of the falling factorial coefficients. Some of their properties are then developed, particularly those in relation to Bernoulli and Stirling numbers and Laguerre polynomials. A partial recurrence relation for the modified Lah numbers is also studied.

Keywords

  • Bernoulli numbers
  • Fibonacci polynomials
  • Laguerre polynomials
  • Lah numbers
  • Lucas polynomials
  • Stirling numbers.

AMS Classification

  • 11B73
  • 05A10

References

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  3. L. Carlitz. “A problem in partitions related to the Stirling numbers.” Bulletin of the American Mathematical Society 70 (1964): 275-278.
  4. L. Carlitz. “Extended Stirling and exponential numbers.” Duke Mathematical Journal 32 (1965): 205-224.
  5. L. Carlitz. “Some partition problems related to the Stirling numbers of the second kind.” Acta Arithmetica 10 (1965): 409-422.
  6. L. Carlitz. “The coefficients in an asymptotic expansion and certain related numbers.” Duke Mathematical Journal 35 (1965): 83-90.
  7. L. Carlitz. “Some generating functions for Laguerre polynomials.” Duke Mathematical Journal 35 (1968): 825-828.
  8. H. W. Gould. “The q-Stirling numbers of first and second kinds.” Duke Mathematical Journal 28 (1961): 281-289.
  9. M. V. Koutras. “Eulerian numbers associated with sequences of polynomials.” Fibonacci Quarterly 32 (1994): 44-57.
  10. J. Riordan. Combinatorial Identities. New York: Wiley, 1968.
  11. S. Tauber. “Lah numbers for Fibonacci and Lucas polynomials.” Fibonacci Quarterly 6 (1968): 93-99.

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Cite this paper

Shannon, A. (2001). Some properties of modified Lah numbers. Notes on Number Theory and Discrete Mathematics, 7(4), 125-131.

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