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Convoluted convolved Fibonacci numbers

Pieter Moree
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Abstract

The convolved Fibonacci numbers F_j^(r) are defined by (1-z-z^2)^{-r}=\sum_{j>=0}F_{j+1}^(r)z^j. In this note some related numbers that can be expressed in terms of convolved Fibonacci numbers are considered. These numbers appear in the numerical evaluation of a certain number theoretical constant. This note is a case study of the transform {1/n}\sum_{d|n}mu(d)f(z^d)^{n/d}, with f any formal series and mu the Moebius function), which is studied in a companion paper entitled `The formal series Witt transform'.

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Pieter Moree. 2003-11-12. Convoluted convolved Fibonacci numbers. https://arxiv.org/abs/math/0311205

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