Geodesic
A note on the Hankel transform of the central binomial coefficients
Journal of integer sequences, Tome 11 (2008) no. 5
We show that the $n\times n$ Hankel matrix formed from the successive even central binomial coefficients ${2l \choose l}, l=0, 1,\dots$ 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.
Classification : 11B83, 11R04
Keywords: Hankel transform, Hankel matrix, central binomial coefficients, trace forms, ring of algebraic integers 
@article{JIS_2008__11_5_a2,
     author = {Garcia Armas,  Mario and Sethuraman,  B.A.},
     title = {A note on the {Hankel} transform of the central binomial coefficients},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {5},
     zbl = {1196.11046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_5_a2/}
}
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Garcia Armas,  Mario; Sethuraman,  B.A. A note on the Hankel transform of the central binomial coefficients. Journal of integer sequences, Tome 11 (2008) no. 5. http://geodesic.mathdoc.fr/item/JIS_2008__11_5_a2/