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A326529 Sum of the fourth largest parts of the partitions of n into 9 squarefree parts.

%I A326529 #5 Jul 12 2019 07:19:25
%S A326529 0,0,0,0,0,0,0,0,0,1,1,2,2,5,7,11,14,22,28,40,47,67,80,107,125,167,
%T A326529 197,257,298,387,455,575,663,834,964,1185,1353,1648,1882,2263,2553,
%U A326529 3045,3438,4054,4542,5331,5965,6936,7716,8936,9936,11434,12646,14504
%N A326529 Sum of the fourth largest parts of the partitions of n into 9 squarefree parts.
%H A326529 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326529 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 * k, where mu is the Möbius function (A008683).
%F A326529 a(n) = A326523(n) - A326524(n) - A326525(n) - A326526(n) - A326527(n) - A326528(n) - A326530(n) - A326531(n) - A326532(n).
%t A326529 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k * MoebiusMu[q]^2 * MoebiusMu[p]^2 * MoebiusMu[o]^2 * MoebiusMu[m]^2 * MoebiusMu[l]^2 * MoebiusMu[k]^2 * MoebiusMu[j]^2 * MoebiusMu[i]^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, 80}]
%Y A326529 Cf. A008683, A326522, A326523, A326524, A326525, A326526, A326527, A326528, A326530, A326531, A326532.
%K A326529 nonn
%O A326529 0,12
%A A326529 _Wesley Ivan Hurt_, Jul 11 2019