What is $\sum_{k=0}^{n} {n \choose k}^3$

Asked Oct 11 '21 at 19:54

Active Oct 13 '21 at 02:27

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Having a little trouble determining if there is a closed form expression for $\sum_{k=0}^{n} {n \choose k}^3$.

Trying to solve a larger problem from Peter Cameron's Combinatorics book (Dixon's Identity) and trying to determine this identity to help with it.

edited Oct 13 '21 at 02:27

asked Oct 11 '21 at 19:54

mobius314

2

What are your thoughts on the matter? What have you tried? Where did you get stuck? Have you computed some small values? – Servaes Oct 11 '21 at 19:56
Ya I tried computing some small values, the main problem I'm trying to solve is from Peter Cameron's Combinatorics book, and I'm trying to determine this identity to help with that question. – mobius314 Oct 11 '21 at 20:01
1

Calculate the first few values & then consult OEIS. https://oeis.org/A000172 ... Good luck. – Donald Splutterwit Oct 11 '21 at 20:01
Thanks @DonaldSplutterwit – mobius314 Oct 11 '21 at 20:04
https://artofproblemsolving.com/community/c6h1352001p7387371 – Jean Marie Oct 11 '21 at 20:07
Thanks @JeanMarie – mobius314 Oct 11 '21 at 20:11

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