  We deliver here second new $\textit{H(x)}-binomials'$ recurrence formula,
were $H(x)-binomials' $ 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{\"{o}}rgy P\'olya $ and Donald Ervin Knuth relevant investigation decades
ago.
