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 A308844 #14 Nov 19 2022 21:43:04
%S A308844 0,0,0,0,0,1,1,3,4,8,10,16,18,29,33,52,59,83,93,125,138,178,196,252,
%T A308844 275,350,380,471,506,634,689,839,901,1096,1176,1405,1484,1767,1861,
%U A308844 2199,2294,2695,2823,3281,3388,3941,4101,4714,4901,5607,5843,6643,6893
%N A308844 Sum of the second largest parts in the partitions of n into 5 squarefree parts.
%H A308844 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308844 a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l)^2 * i, where mu is the Möbius function (A008683).
%F A308844 a(n) = A308839(n) - A308841(n) - A308842(n) - A308843(n) - A308845(n).
%e A308844 The partitions of n into 5 parts for n = 10, 11, ..
%e A308844 1+1+1+1+10
%e A308844 1+1+1+2+9
%e A308844 1+1+1+3+8
%e A308844 1+1+1+4+7
%e A308844 1+1+1+5+6
%e A308844 1+1+1+1+9 1+1+2+2+8
%e A308844 1+1+1+2+8 1+1+2+3+7
%e A308844 1+1+1+3+7 1+1+2+4+6
%e A308844 1+1+1+4+6 1+1+2+5+5
%e A308844 1+1+1+5+5 1+1+3+3+6
%e A308844 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
%e A308844 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
%e A308844 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
%e A308844 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
%e A308844 1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
%e A308844 1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
%e A308844 1+1+1+1+6 1+1+1+4+4 1+1+2+4+4 1+2+2+3+5 1+2+3+4+4
%e A308844 1+1+1+2+5 1+1+2+2+5 1+1+3+3+4 1+2+2+4+4 1+3+3+3+4
%e A308844 1+1+1+3+4 1+1+2+3+4 1+2+2+2+5 1+2+3+3+4 2+2+2+2+6
%e A308844 1+1+2+2+4 1+1+3+3+3 1+2+2+3+4 1+3+3+3+3 2+2+2+3+5
%e A308844 1+1+2+3+3 1+2+2+2+4 1+2+3+3+3 2+2+2+2+5 2+2+2+4+4
%e A308844 1+2+2+2+3 1+2+2+3+3 2+2+2+2+4 2+2+2+3+4 2+2+3+3+4
%e A308844 2+2+2+2+2 2+2+2+2+3 2+2+2+3+3 2+2+3+3+3 2+3+3+3+3
%e A308844 --------------------------------------------------------------------------
%e A308844 n | 10 11 12 13 14 ...
%e A308844 --------------------------------------------------------------------------
%e A308844 a(n) | 10 16 18 29 33 ...
%e A308844 --------------------------------------------------------------------------
%e A308844 - _Wesley Ivan Hurt_, Sep 16 2019
%t A308844 Table[Total[Select[IntegerPartitions[n,{5}],AllTrue[#,SquareFreeQ]&][[All,2]]],{n,0,60}] (* _Harvey P. Dale_, Nov 19 2022 *)
%Y A308844 Cf. A008683, A308839, A308840, A308841, A308842, A308843, A308845.
%K A308844 nonn
%O A308844 0,8
%A A308844 _Wesley Ivan Hurt_, Jun 28 2019