Elsevier

Linear Algebra and its Applications

Volumes 226–228, September–October 1995, Pages 57-72
Linear Algebra and its Applications

Some canonical sequences of integers

Dedicated to J. J. Seidel
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Abstract

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(ex − 1) + 1.

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