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%I A308956 #6 Jul 03 2019 06:12:43
%S A308956 0,0,0,0,0,0,0,1,1,2,2,4,6,10,12,16,20,30,34,46,52,71,80,103,115,149,
%T A308956 167,211,236,298,332,410,457,559,619,742,814,981,1078,1269,1384,1633,
%U A308956 1786,2072,2246,2607,2839,3267,3524,4050,4379,4970,5350,6076,6555
%N A308956 Sum of the fifth largest parts in the partitions of n into 7 squarefree parts.
%H A308956 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308956 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 * l, where mu is the Möbius function (A008683).
%F A308956 a(n) = A308953(n) - A308954(n) - A308955(n) - A308957(n) - A308958(n) - A308959(n) - A308960(n).
%t A308956 Table[Sum[Sum[Sum[Sum[Sum[Sum[l * 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}]
%Y A308956 Cf. A008683, A308952, A308953, A308954, A308955, A308957, A308958, A308959, A308960.
%K A308956 nonn
%O A308956 0,10
%A A308956 _Wesley Ivan Hurt_, Jul 03 2019

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