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Fixed Sequences for a Generalization of the Binomial Interpolated Operator
and for some Other Operators
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Marco Abrate, Stefano Barbero, Umberto Cerruti, and Nadir Murru

Department of Mathematics

University of Turin

via Carlo Alberto 8/10

Turin

Italy

**Abstract:**

This paper is devoted to the study of eigen-sequences for some
important operators acting on sequences. Using functional equations
involving generating functions, we completely solve the problem of
characterizing the fixed sequences for the Generalized Binomial operator.
We give some applications to integer sequences. In particular we show
how we can generate fixed sequences for Generalized Binomial and their
relation with the Worpitzky transform. We illustrate this fact with
some interesting examples and identities, related to Fibonacci,
Catalan, Motzkin and Euler numbers. Finally we find the eigen-sequences
for the mutual compositions of the operators Interpolated Invert,
Generalized Binomial and Revert.

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(Concerned with sequences
A000045
A000108
A000984
A001006
A001850
A101890
A115865
A155585.)

Received April 10 2011;
revised version received August 2 2011.
Published in *Journal of Integer Sequences*, September 25 2011.

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