$\mathcal D^K_{\lambda/2} [F_{j_1, \dots, j_N;l_1, \dots, l_N}(\lambda)]$ has the sense of the number of trajectories of $N$ vicious walkers each of which has made $K$ steps. A different combinatorial interpretation of this object, however, can be proposed. Really, let us consider a representation of the multi-point correlator in the form of the determinant . Its entries $F_{j_r;l_s}(\lambda)$ in the case of an infinite chain are given by the Bessel function $I_{j_r-l_s}(\lambda)$ . The operator $\mathcal D^K_{\lambda/2}$ acts on the determinant as the differentiation of the product of $N$ functions: $$(f_1(x)f_2(x)\dots f_N(x))^{(K)}=
\sum_{n_1+n_2+\dots+n_N=K}P(n_1,n_2,\dots,n_N)
f^{(n_1)}_1f^{(n_2)}_2\dots f^{(n_N)}_N.
\label{27}$$ The notation $f^{(n)}\equiv d^nf(x)/dx^n$ is used here, and the coefficients $P(n_1,n_2,\dots,n_N)$ are the numbers of permutations with repeats: $$P(n_1,n_2,\dots,n_N)\equiv
\frac{(n_1+n_2+\dots+n_N)!}{n_1!\,n_2!\,\dots n_N!}.
\label{28}$$ Summation in  is over all non-negative values of $n_1,n_2,\dots,n_N$, provided their sum is equal to $K$.

Suppose further, that an $N$-dimensional (hyper-)cubic lattice of infinite extension is given, and each site of this lattice is labelled by a set of $N$ numbers. Let $\mathcal T_K(q_1,q_2, \dots
,q_N)$ be the number of the lattice trajectories that can be traced by some walker from the “initial” point $\textbf{\textit{O}}\equiv(0,0, \dots, 0)$ to a point $(q_1,q_2,\dots,q_N)$ in $K$ steps (by a single step the walker can move 