  We revisit the derivation of a formula for the $q$-generalised multinomial
coefficient rooted in the $q$-deformed algebra, a foundational framework in the
study of nonextensive statistics. Previous approximate expressions in the
literature diverge as $q$ approaches 2 (or 0, depending on convention). In
contrast, our derived formula provides an exact, smooth function for all real
values of $q$, expressed as an infinite series expansion involving Tsallis
entropies with sequential entropic indices, coupled with Bernoulli numbers.
This formulation is achieved through the analytic continuation of the Riemann
zeta function, stemming from the $q$-deformed factorials. Thus, our formula
offers a distinctive characterisation of Tsallis entropy within the
$q$-deformed combinatorics. Furthermore, we discuss extending our results to
encompass more general, affinity-sensitive cases based on the previously
established framework of affinity-based extended entropy.
