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A326631
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Sum of the seventh largest parts of the partitions of n into 10 squarefree parts.
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11
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 10, 15, 19, 28, 33, 45, 55, 73, 86, 113, 132, 171, 198, 250, 288, 359, 411, 504, 578, 700, 798, 961, 1090, 1306, 1477, 1752, 1976, 2338, 2625, 3080, 3457, 4029, 4508, 5228, 5831, 6733, 7490, 8594, 9547
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OFFSET
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0,13
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LINKS
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FORMULA
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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 * o, where mu is the Möbius function (A008683).
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MATHEMATICA
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Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[o * MoebiusMu[r]^2 * 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 - r]^2 , {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 50}]
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CROSSREFS
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Cf. A008683, A326626, A326627, A326628, A326629, A326630, A326632, A326633, A326634, A326635, A326636, A326637.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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