How can this summation be written in terms of hypergeometric function?

Asked Feb 15 '16 at 14:22

Active Feb 15 '16 at 14:25

Viewed 78 times

I came across an expression as

\begin{equation} \sum_{k=0}^n(-1)^k\binom{2n}{k}(n-k)^{2n-1}. \end{equation}

It seems similar to the definition of the hypergeometric function, is it possible to rewrite it into the hypergeometric function?

Thanks a lot!

edited Feb 15 '16 at 14:25

asked Feb 15 '16 at 14:22

Alex

1

it corresponds more to the Generalized_hypergeometric_function – reuns Feb 15 '16 at 15:03
1

See OEIS A$25585$. – Lucian Feb 15 '16 at 18:47
@user1952009, could you please elaborate a little bit since I am not familiar with this kind of function. Thanks a lot! – Alex Feb 16 '16 at 02:19

0 Answers0