which is a reformulation of (\[eq.2\]): $$4^n=
\sum_{k=0}^n \, {(k+1)^2 \over n+1} \, {2n+2\choose n-k}.$$ Let $p$ be an integer with $0\leq p\leq j$. The [*elevation*]{} of $P$ with respect to the horizontal line $y=p$ is defined as follows. For $p=0$, the elevation of $P$ with respect to $y=0$ is just $P$ itself. We now assume $ 0<p\leq j$. Note that there are always up steps of $P$ at levels $j-1$, $j-2$, …, $0$ bearing in mind that an up step is said to be at level $k$ if its initial point is at level $k$. Therefore, for each level from $0$ to $p-1$, one can find a rightmost up step. Note that there are no other steps at the same level to the right of the rightmost up step which is called a [*R-visible*]{} up step with respect to the line $y=p$ in the sense that it can seen far away from the right. The elevation of $P$ with respect to the line $y=p$ is derived from $P$ by changing the R-visible up steps up to level $p-1$ to down steps by elevating their initial points. The line $y=p$ is called an [*elevation line*]{}.

Figure \[mot\] is an illustration 