Given a sequence $A_n(k)$ defined as follows:

$A_0(0)=1$, $A_0(k)=0$ for all nonzero integers $k$ and $$A_{n}(k)=(n+1-k)^2A_{n-1}(k-1)+2(n(n+1)-k^2)A_{n-1}(k)+(n+1+k)^2A_{n-1}(k+1)$$ for all positive integers $n$ and integers $k$. Does there exist an explicit formula for $A_n(k)$? This sequence is related to the function values of the uniform cardinal B-splines at the integers.

Thanks for any help in advance

Markus