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%I A308958 #6 Jul 03 2019 06:12:57
%S A308958 0,0,0,0,0,0,0,1,1,2,3,6,8,14,17,25,30,44,50,72,83,115,136,184,213,
%T A308958 278,321,409,463,579,650,807,900,1089,1215,1462,1610,1926,2133,2520,
%U A308958 2772,3258,3586,4195,4587,5327,5847,6780,7376,8513,9283,10639,11538,13168
%N A308958 Sum of the third largest parts in the partitions of n into 7 squarefree parts.
%H A308958 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308958 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 * j, where mu is the Möbius function (A008683).
%F A308958 a(n) = A308953(n) - A308954(n) - A308955(n) - A308956(n) - A308957(n) - A308959(n) - A308960(n).
%t A308958 Table[Sum[Sum[Sum[Sum[Sum[Sum[j * 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 A308958 Cf. A008683, A308952, A308953, A308954, A308955, A308956, A308957, A308959, A308960.
%K A308958 nonn
%O A308958 0,10
%A A308958 _Wesley Ivan Hurt_, Jul 03 2019

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