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 A353021 #26 Jun 14 2022 08:51:13
%S A353021 0,1,341,13013,196053,1733303,10787231,52253971,209609235,725520510,
%T A353021 2230238010,6217887390,15973440990,38276304066,86383520146,
%U A353021 185042663146,378620563178,743881306623,1409531082531,2585397711611,4605062303611
%N A353021 a(n) = Sum_{l=1..n} Sum_{k=1..l} Sum_{j=1..k} Sum_{i=1..j} (l*k*j*i)^2.
%C A353021 a(n) is the sum of all products of four squares of positive integers up to n, i.e., the sum of all products of four elements from the set of squares {1^2, ..., n^2}.
%H A353021 Roudy El Haddad, <a href="https://arxiv.org/abs/2101.09089">Recurrent Sums and Partition Identities</a>, arXiv:2101.09089 [math.NT], 2021.
%H A353021 Roudy El Haddad, <a href="https://doi.org/10.7546/nntdm.2022.28.2.167-199">A generalization of multiple zeta value. Part 1: Recurrent sums</a>, Notes on Number Theory and Discrete Mathematics, 28(2), 2022, 167-199, DOI: 10.7546/nntdm.2022.28.2.167-199. See Theorem 4.8 for m = 4 and p = 2.
%H A353021 <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).
%F A353021 a(n) = n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(2*n + 1)*(2*n + 3)*(2*n + 5)*(2*n + 7)*(5*n - 2)*(35*n^2 - 28*n + 9)/5443200.
%F A353021 a(n) = binomial(2*n+8,9)*(5*n - 2)*(35*n^2 - 28*n + 9)/(5!*4).
%o A353021 (PARI) {a(n) = n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(2*n + 1)*(2*n + 3)*(2*n + 5)*(2*n + 7)*(5*n - 2)*(35*n^2 - 28*n + 9)/5443200};
%o A353021 (Python)
%o A353021 def A353021(n): return n*(n*(n*(n*(n*(n*(n*(n*(8*n*(n*(70*n*(5*n + 84) + 40417) + 144720) + 2238855) + 2050020) + 207158) - 810600) - 58505) + 322740) + 7956) - 45360)//5443200 # _Chai Wah Wu_, May 14 2022
%Y A353021 Cf. A354021 (for distinct squares).
%Y A353021 Cf. A000290 (squares), A000330 (sum of squares), A060493 (for two squares), A351105 (for three squares).
%Y A353021 Cf. A000915 (for power 1).
%K A353021 nonn,easy
%O A353021 0,3
%A A353021 _Roudy El Haddad_, Apr 17 2022