Some Canonical Sequences of Integers

Details Some Canonical Sequences of Integers Some Canonical Sequences of Integers

2002-05-28

arxiv.org/abs/math/0205301v1

Linear Algebra and its Applications, Vol. 226-228 (1995), pp. 57-72; errata Vol. 320 (2000), p. 210

Mathematics

Combinatorics

18 pages, 2 figures; Dedicated to Professor J. J. Seidel

Scientific paper

Extending earlier work of R. Donaghey and P. J. Cameron, we investigate some canonical "eigen-sequences" associated with transformations of integer sequences. Several known sequences appear in a new setting: for instance the sequences (such as 1, 3, 11, 49, 257, 1531, ...) studied by T. Tsuzuku, H. O. Foulkes and A. Kerber in connection with multiply transitive groups are eigen-sequences for the binomial transform. Many interesting new sequences also arise, such as 1, 1, 2, 26, 152, 1144, ..., which shifts one place left when transformed by the Stirling numbers of the second kind, and whose exponential generating function satisfies A'(x) = A(e^x -1) + 1.

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