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Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 373927, 10 pages
http://dx.doi.org/10.1155/2013/373927
Research Article

Sums of Products of Cauchy Numbers, Including Poly-Cauchy Numbers

Graduate School of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan

Received 24 July 2012; Accepted 24 October 2012

Academic Editor: Gi Sang Cheon

Copyright © 2013 Takao Komatsu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Comtet, Advanced Combinatorics, Reidel, Doredecht, The Netherland, 1974. View at MathSciNet
  2. T. Agoh and K. Dilcher, “Recurrence relations for nörlund numbers and bernoulli numbers of the second kind,” Fibonacci Quarterly, vol. 48, no. 1, pp. 4–12, 2010. View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. P. T. Young, “A 2-adic formula for Bernoulli numbers of the second kind and for the Nörlund numbers,” Journal of Number Theory, vol. 128, no. 11, pp. 2951–2962, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. G. S. Cheon, S. G. Hwang, and S. G. Lee, “Several polynomials associated with the harmonic numbers,” Discrete Applied Mathematics, vol. 155, no. 18, pp. 2573–2584, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. M. Liu, S. H. Qi, and S. Y. Ding, “Some recurrence relations for cauchy numbers of the first kind,” Journal of Integer Sequences, vol. 13, no. 3, pp. 1–7, 2010. View at Zentralblatt MATH · View at MathSciNet
  6. D. Merlini, R. Sprugnoli, and M. C. Verri, “The Cauchy numbers,” Discrete Mathematics, vol. 306, no. 16, pp. 1906–1920, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. W. Wang, “Generalized higher order Bernoulli number pairs and generalized Stirling number pairs,” Journal of Mathematical Analysis and Applications, vol. 364, no. 1, pp. 255–274, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. Z. Zhao, “Sums of products of Cauchy numbers,” Discrete Mathematics, vol. 309, no. 12, pp. 3830–3842, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Kaneko, “Poly-Bernoulli numbers,” Journal de Théorie des Nombres de Bordeaux, vol. 9, pp. 199–206, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, Mass, USA, 2nd edition, 1994. View at MathSciNet
  11. T. Agoh and K. Dilcher, “Shortened recurrence relations for Bernoulli numbers,” Discrete Mathematics, vol. 309, no. 4, pp. 887–898, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. T. Komatsu, “Poly-Cauchy numbers,” Kyushu Journal of Mathematics, vol. 67, 2013.
  13. K. Kamano and T. Komatsu, “Poly-Cauchy polynomials,” In preparation.
  14. K. Kamano, “Sums of products of Bernoulli numbers, including poly-Bernoulli numbers,” Journal of Integer Sequences, vol. 13, no. 5, pp. 1–10, 2010. View at Zentralblatt MATH · View at MathSciNet · View at Scopus