A Note on the Hankel Transform of the Central Binomial Coefficients
Mario Garcia Armas
Facultad de Matemática y Computación
Universidad de La Habana
B. A. Sethuraman
Dept. of Mathematics
California State University, Northridge
Northridge, CA 91330
We show that the
Hankel matrix formed from the successive
even central binomial coefficients
arises naturally when considering the trace form in the number ring of
the maximal real subfield of suitable cyclotomic fields. By considering
the trace form in two different integral bases of the number ring we
get a factorization of this matrix which immediately yields the
well-known zeroth and first Hankel transforms of the sequence.
Full version: pdf,
(Concerned with sequence
Received November 10 2008;
revised version received November 25 2008.
Published in Journal of Integer Sequences, December 14 2008.
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