  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.
