Converting between generalized Bell, Lah, Stirling, and Tanh numbers

Journal of Integer Sequences

Volumn 9, Issue 3, 2006, Pages 1-9

  Della Riccia, Giacomo ^a  

^a UNIVERSITY OF UDINE   (Italy)

Author keywords

Bell triangle; Conversions; Riordan group

Indexed keywords

EID: 33746300809     PISSN: 15307638     EISSN: 15307638     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. N. T. Cameron and A. Nkwanta, On some (pseudo) involutions in the Riordan group, J. Integer Seq. 8 (2005), 1-16, Article 05.3.7.
2. L. Carlitz, Some remarks on the Bell numbers, Fibonacci Quart. 18 (1980), 66-73.
3. M. Cohn, S. Even, K. Menger, Jr., and P. K. Hooper, On the number of partitionings of a set of n distinct objects, Amer. Math. Monthly 69 (1962), 782-785.
4. L. Comtet, Advanced Combinatorics, Riedel, Dordrecht, 1974.
5. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Sciences, Addison-Wesley, 1994.
6. M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Seq. 3 (2000), 1-6, Article 00.2.9.
7. D. E. Knuth, The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, 1973.
8. I. Lah, Eine neue Art von Zahlen, ihre Eigenschaften und Anwendung in der mathematischen Statistik, Mitteilungsbl. Math. Statis. 7 (1955), 203-216.
9. k the Stirling numbers of the second kind, Discrete Math. 150 (1996), 281-292.
10. D. Merlini, R. Sprugnoli and M. C. Verri, The Akimaya-Tanigawa transformation, Integers: Electronic J. of Combinatorial Number Theory 5 (2005), no. 1, A05, 12pp.
11. J. Riordan, An Introduction to Combinatorial Analysis, Princeton University Press, 1980.
12. D. G. Rogers, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math. 22 (1978), 301-310.
13. J. Shallit, A triangle for the Bell numbers, in Verner E. Hoggatt and Marjorie Bicknell-Johnson, eds., A Collection of Manuscripts Related to the Fibonacci Sequence, 18th Anniversary Volume, Fibonacci Association, Santa Clara, Calif., 1980, pp. 69-71.
14. L. W. Shapiro, Bijections and the Riordan group, Theoret. Comp. Sci. 307 (2003), 403-413.
15. L. W. Shapiro, S. Getu, W-J. Woan, and L. C. Woodson, The Riordan group, Discrete Appl. Math. 34 (1991), 229-239.
16. R. Sprugnoli, Riordan arrays and combinatorial sums, Discrete Math. 132 (1994), 267-290.
17. R. Sprugnoli, Riordan arrays and the Abel-Gould identity, Discrete Math. 142 (1995), 213-233.
18. K.-W. Chen, Algorithms for Bernoulli numbers and Euler numbers, J. Integer Sequences, 4 (2001), paper no. 01.1.6.
19. X. Zhao and T. Wang, Some identities related to reciprocal functions, Discrete Math. 265 (2003), 323-335.