Hi,
I was in touch with Mathematica development team and they indicated that
currently Mathematica is not capable to determine whether
Sum[Binomial[n - 1, n - i] Sum[Binomial[k + i, i] Binomial[n - 1, n - k],
{k, 0, n}], {i, 0, n}]
= ?
(-1)^n*((-4*n^2 - 16*n - 28)*JacobiP[-1 + n, -1 - 2*n, 2, -1/2] +
JacobiP[-2 + n, -2*n, 3, -1/2]*(3 + n)*(-1 + n))*4^n/(48*(1 + n)*n)
Could you check whether Sage has such capability?
Thanks,
Best regards,
Alexander R. Povolotsky
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