This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352980 #30 Sep 30 2022 06:02:06
%S A352980 0,0,0,216,16280,335655,3587535,25421200,135459216,584760870,
%T A352980 2145870870,6918983280,20073184560,53334782501,131555523645,
%U A352980 304453955520,666698215360,1390977293580,2780695001196,5351537889480,9954554649480,17957698726275
%N A352980 a(n) = Sum_{1 <= i < j < k <= n} (k*j*i)^3.
%C A352980 a(n) is the sum of all products of three distinct cubes of positive integers up to n, i.e., the sum of all products of three distinct elements from the set of cubes {1^3, ..., n^3}.
%H A352980 Roudy El Haddad, <a href="https://arxiv.org/abs/2102.00821">Multiple Sums and Partition Identities</a>, arXiv:2102.00821 [math.CO], 2021.
%H A352980 Roudy El Haddad, <a href="https://doi.org/10.7546/nntdm.2022.28.2.200-233">A generalization of multiple zeta value. Part 2: Multiple sums</a>. Notes on Number Theory and Discrete Mathematics, 28(2) 2022, 200-233, DOI: 10.7546/nntdm.2022.28.2.200-233. See Theorem 5.1 for m = 3 and p = 3.
%H A352980 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1). [Typo corrected by _Georg Fischer_, Sep 30 2022]
%F A352980 a(n) = Sum_{k=3..n} Sum_{j=2..k-1} Sum_{i=1..j-1} k^3*j^3*i^3.
%F A352980 a(n) = n^2 * (n + 1)^2 * (n - 1) * (n - 2) * (35*n^6 + 5*n^5 - 237*n^4 - 77*n^3 + 502*n^2 + 148*n -336)/13440.
%F A352980 a(n) = binomial(n+1,4)*binomial(n+1,2)*(35*n^6 + 5*n^5 - 237*n^4 - 77*n^3 + 502*n^2 + 148*n -336)/280.
%o A352980 (PARI) {a(n) = n^2 * (n + 1)^2 * (n - 1) * (n - 2) * (35*n^6 + 5*n^5 - 237*n^4 - 77*n^3 + 502*n^2 + 148*n -336)/13440};
%o A352980 (Python)
%o A352980 def A352980(n): return n**2*(n*(n*(n*(n*(n*(n*(n*(n*(n*(35*n - 30) - 347) + 180) + 1365) - 350) - 2541) + 240) + 2160) - 40) - 672)//13440 # _Chai Wah Wu_, May 15 2022
%Y A352980 Cf. A352979 (for nondistinct cubes).
%Y A352980 Cf. A001303 (for power 1), A000597 (for squares).
%Y A352980 Cf. A000578 (cubes), A000537 (sum of first n cubes), A347107 (order 2).
%K A352980 nonn,easy
%O A352980 0,4
%A A352980 _Roudy El Haddad_, Apr 13 2022