For $i,j=1,2,\ldots$ consider the polynomials $c_{i,j}(x)=(x+i)^{j}-(x+i-1)^{j}$ ($x$ is the indeterminate). Then, for every positive natural number $n$ $$ \det (c_{i,j})_{i,j=1}^n = \prod_{k=1}^{n} k! $$