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 A326525 #9 Jan 30 2024 22:24:05
%S A326525 0,0,0,0,0,0,0,0,0,1,1,2,2,4,5,8,9,14,18,24,28,39,46,60,69,90,105,133,
%T A326525 149,189,216,264,297,364,412,494,553,661,743,877,972,1149,1280,1493,
%U A326525 1650,1922,2126,2454,2702,3107,3429,3916,4291,4895,5374,6086,6647
%N A326525 Sum of the eighth largest parts in the partitions of n into 9 squarefree parts.
%H A326525 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326525 a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/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)^2 * p, where mu is the Möbius function (A008683).
%F A326525 a(n) = A326523(n) - A326524(n) - A326526(n) - A326527(n) - A326528(n) - A326529(n) - A326530(n) - A326531(n) - A326532(n).
%t A326525 Table[Total[Select[IntegerPartitions[n,{9}],AllTrue[#,SquareFreeQ]&][[;;,8]]],{n,0,60}] (* _Harvey P. Dale_, Jan 30 2024 *)
%Y A326525 Cf. A008683, A326522, A326523, A326524, A326526, A326527, A326528, A326529, A326530, A326531, A326532.
%K A326525 nonn
%O A326525 0,12
%A A326525 _Wesley Ivan Hurt_, Jul 11 2019