Sage

[Alexander P-sky]

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