A308959 Sum of the second largest parts in the partitions of n into 7 squarefree parts.
0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 4, 8, 10, 18, 22, 34, 41, 65, 78, 111, 129, 179, 213, 277, 315, 412, 476, 602, 674, 849, 966, 1197, 1341, 1645, 1857, 2251, 2496, 3014, 3361, 3995, 4391, 5205, 5731, 6722, 7323, 8538, 9331, 10791, 11678, 13468, 14616, 16687
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[Sum[Sum[Sum[Sum[Sum[i * 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]^2, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]
Formula
a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/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)^2 * i, where mu is the Möbius function (A008683).