Sur certaines sommes binomiales (Q1156134)

The following two identities are proved \((n\geq 1,\;1\geq q\geq 0)\): \[ \sum_{k=0}^{l-q}\binom{n+2l-k-1}{2l-k} \binom{2l-k}{2l-2k}\binom{2l-2k}{l-k+1}=\binom{n+l-q-1}{n-1}\binom{n+l+q-1}{n-1} \] and \[ \sum_{k=0}^{l-q+1}(-1)^k\binom{n+2l-k}{2l-k+1} \binom{2l-k+1}{2l-2k+1}\binom{2l-2k+1}{l-k+q}=\binom{n+l+q-1}{n-1}\binom{n+l-q}{n-1}. \]