  For any integer $r\ge2$, define a sequence of numbers
$\{c_k^{(r)}\}_{k=0}^\infty$, independent of the parameter $n$, by $$
\sum_{k=0}^n{\binom nk}^r{\binom{n+k}k}^r =\sum_{k=0}^n\binom
nk\binom{n+k}kc_k^{(r)}, \qquad n=0,1,2,...c. $$ We prove that all the numbers
$c_k^{(r)}$ are integers.
