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 A308908 #7 Jun 29 2019 23:03:06
%S A308908 0,0,0,0,0,0,1,1,2,2,5,7,11,12,18,22,32,34,47,52,71,78,102,116,154,
%T A308908 170,217,243,305,329,406,445,546,587,702,768,921,982,1147,1240,1459,
%U A308908 1562,1811,1948,2260,2401,2748,2943,3387,3596,4087,4381,4987,5288,5959
%N A308908 Sum of the fourth largest parts in the partitions of n into 6 squarefree parts.
%H A308908 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308908 a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-k-j-l-m)^2 * k, where mu is the Möbius function (A008683).
%F A308908 a(n) = A308903(n) - A308906(n) - A308907(n) - A308909(n) - A308910(n) - A308911(n).
%t A308908 Table[Sum[Sum[Sum[Sum[Sum[k*MoebiusMu[i]^2*MoebiusMu[j]^2*MoebiusMu[k]^2* MoebiusMu[l]^2*MoebiusMu[m]^2*MoebiusMu[n - i - j - k - l - m]^2, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
%Y A308908 Cf. A008683, A308902, A308903, A308906, A308907, A308909, A308910, A308911.
%K A308908 nonn
%O A308908 0,9
%A A308908 _Wesley Ivan Hurt_, Jun 29 2019