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 A326636 #14 Jan 05 2023 21:41:49
%S A326636 0,0,0,0,0,0,0,0,0,0,1,1,3,4,8,10,18,22,36,45,72,88,127,153,215,263,
%T A326636 351,418,555,658,843,984,1252,1460,1825,2118,2623,3029,3697,4248,5168,
%U A326636 5914,7101,8088,9676,10960,12974,14647,17246,19396,22653,25384,29527
%N A326636 Sum of the second largest parts of the partitions of n into 10 squarefree parts.
%H A326636 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326636 a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} mu(r)^2 * mu(q)^2 * mu(p)^2 * mu(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o-p-q-r)^2 * i, where mu is the Möbius function (A008683).
%F A326636 a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326631(n) - A326632(n) - A326633(n) - A326634(n) - A326635(n) - A326637(n).
%t A326636 Table[Total[Select[IntegerPartitions[n,{10}],AllTrue[#,SquareFreeQ]&][[All,2]]],{n,0,55}] (* _Harvey P. Dale_, Jan 03 2023 *)
%Y A326636 Cf. A008683, A326626, A326627, A326628, A326629, A326630, A326631, A326632, A326633, A326634, A326635, A326637.
%K A326636 nonn
%O A326636 0,13
%A A326636 _Wesley Ivan Hurt_, Jul 14 2019