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%I #5 Aug 03 2019 21:47:47
%S 0,0,0,0,0,0,0,0,0,9,9,18,26,44,61,95,128,187,252,343,446,600,765,995,
%T 1256,1600,1987,2493,3053,3772,4583,5582,6712,8103,9657,11534,13649,
%U 16165,18987,22324,26041,30401,35269,40899,47174,54414,62432,71612,81791
%N Number of squarefree parts in the partitions of n into 9 parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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), where mu is the Möbius function (A008683).
%t Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(MoebiusMu[i]^2 + MoebiusMu[j]^2 + MoebiusMu[k]^2 + MoebiusMu[l]^2 + MoebiusMu[m]^2 + MoebiusMu[o]^2 + MoebiusMu[p]^2 + MoebiusMu[q]^2 + MoebiusMu[n - i - j - k - l - m - o - p - q]^2), {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]
%Y Cf. A008683.
%K nonn
%O 0,10
%A _Wesley Ivan Hurt_, Aug 03 2019
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