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Abstract

The limit expression, denoted by ����,��(��, ��) was evaluated completely that yields an explicit formula in elementary symmetric function form. The limit ����,��(��, ��) has possessed some necessary properties like recurrence relations, generating functions, orthogonality relation, inverse relation and matrix factorization. It has been identified that the numbers ����,��(��, ��) are certain generalization of Gould-Hopper numbers, which are useful in biology and reliability theory. One can easily verify that these numbers are equivalent to the first kind r-Whitney numbers using their existing properties. In this present paper, a combinatorial meaning for r-Whitney numbers of the first kind in the context of (0, 1)-tableau is constructed using the explicit formula in symmetric function form. Moreover, some convolution-type formulas are derived that, consequently, yield LU-factorization of the matrix whose entries are the first kind r-Whitney numbers.,

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