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0. INTRODUCTION For a natural number vand two sequences {A(k),B(k)} k of binomial coefficients, the following convolutions of Vandermonde type, C(rn, w, v): = ]T A(m + kv)B{n-kv) , k will be investigated in this paper. When v = 2, 3, 4, the convolutions will be nominated duplicate, triplicate, and quadruplicate, respectively. Thanks to the explicit(More)
A Dyck path of length 2n is a path in two-space from (0, 0) to (2n, 0) which uses only steps (1, 1) (northeast) and (1, −1) (southeast). Further, a Dyck path does not go below the x-axis. A peak on a Dyck path is a node that is immediately preceded by a northeast step and immediately followed by a southeast step. A peak is at height k if its y-coordinate is(More)
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(More)