Fibonacci polynomials, generalized Stirling numbers, and Bernoulli, Genocchi and tangent numbers

Mathematics – Combinatorics

Scientific paper

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45 pages

Scientific paper

We study matrices which transform the sequence of Fibonacci or Lucas
polynomials with even index to those with odd index and vice versa. They turn
out to be intimately related to generalized Stirling numbers and to Bernoulli,
Genocchi and tangent numbers and give rise to various identities between these
numbers. There is also a close connection with the Akiyama-Tanigawa algorithm.

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