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**Hankel Matrices and Lattice Paths**

### Wen-Jin Woan

Department of Mathematics

Howard University

Washington, D.C. 20059, USA

Email address: wwoan@howard.edu

**Abstract:**
Let *H* be the Hankel matrix formed from a sequence of real numbers
*S* = {*a*_{0} = 1, *a*_{1},
*a*_{2}, *a*_{3}, ...}, and let *L*
denote the lower triangular matrix
obtained from the Gaussian column reduction of *H*. This paper gives a
matrix-theoretic proof that the associated Stieltjes matrix *S*_{L}
is a tri-diagonal matrix. It is also shown that for any sequence (of nonzero real numbers)
*T* = {*d*_{0} = 1, *d*_{1},
*d*_{2}, *d*_{3}, ...} there are infinitely many sequences such that
the determinant sequence of the Hankel matrix formed from those sequences is
*T*.

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(Mentions sequences
A000108
A001006
A001850.)

Received September 19 2000;
published in *Journal of Integer Sequences*, April 24 2001.

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