  We introduce a generalization of Pascal triangle based on binomial
coefficients of finite words. These coefficients count the number of times a
word appears as a subsequence of another finite word. Similarly to the
Sierpi\'nski gasket that can be built as the limit set, for the Hausdorff
distance, of a convergent sequence of normalized compact blocks extracted from
Pascal triangle modulo $2$, we describe and study the first properties of the
subset of $[0, 1] \times [0, 1]$ associated with this extended Pascal triangle
modulo a prime $p$.
