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A Note on the Hankel Transform of the Central Binomial Coefficients
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Mario Garcia Armas

Facultad de Matemática y Computación

Universidad de La Habana

Havana, Cuba

B. A. Sethuraman

Dept. of Mathematics

California State University, Northridge

Northridge, CA 91330

USA

**Abstract:**

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.

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(Concerned with sequence
A055878.)

Received November 10 2008;
revised version received November 25 2008.
Published in *Journal of Integer Sequences*, December 14 2008.

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