Journal of Integer Sequences, Vol. 18 (2015), Article 15.1.2

Linear Recurrence Sequences and Their Convolutions via Bell Polynomials

Daniel Birmajer
Department of Mathematics
Nazareth College
Rochester, NY 14618

Juan B. Gil and Michael D. Weiner
Department of Mathematics and Statistics
Penn State Altoona
Altoona, PA 16601


We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a basis of sequences that can be obtained as the INVERT transform of the coefficients of the given recurrence relation. For such a basis sequence with generating function Y(t), and for any positive integer r, we give a formula for the convolved sequence generated by Y(t)r and prove that it satisfies an elegant recurrence relation.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000073 A000931 A001628 A001629 A001872 A073778 A228577.)

Received May 29 2014; revised versions received November 28 2014; November 29 2014. Published in Journal of Integer Sequences, December 14 2014.

Return to Journal of Integer Sequences home page