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%I #12 Mar 20 2023 15:19:22
%S 0,0,0,0,0,0,0,0,1,1,2,2,4,5,8,9,13,15,21,24,32,36,47,53,68,75,94,105,
%T 130,143,174,192,231,254,301,330,389,424,495,539,626,678,781,847,970,
%U 1048,1192,1287,1461,1572,1772,1908,2144,2301,2573,2762,3079,3295
%N Number of partitions of n into 8 squarefree parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/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)^2, where mu is the Möbius function (A008683).
%F a(n) = A326444(n)/n for n > 0.
%t Table[Count[IntegerPartitions[n,{8}],_?(AllTrue[#,SquareFreeQ]&)],{n,0,60}] (* _Harvey P. Dale_, Mar 10 2023 *)
%Y Cf. A008683, A326444, A326445, A326446, A326447, A326448, A326449, A326450, A326451, A326452.
%K nonn
%O 0,11
%A _Wesley Ivan Hurt_, Jul 06 2019
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