Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II

Abstract

We deliver here second new $\text{H(x)}-binomial{s}^{\prime }$ recurrence formula, were $H(x)-binomial{s}^{\prime }$ array is appointed by $Ward-Horadam$ sequence of functions which in predominantly considered cases where chosen to be polynomials . Secondly, we supply a review of selected related combinatorial interpretations of generalized binomial coefficients. We then propose also a kind of transfer of interpretation of $p,q-binomial$ coefficients onto $q-binomial$ coefficients interpretations thus bringing us back to $Gy\ddot{o}rgyP\acute{o}lya$ and Donald Ervin Knuth relevant investigation decades ago.

57 pages, 8 figures

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