%I #6 Jul 06 2019 20:58:37
%S 0,0,0,0,0,0,0,0,1,1,3,4,8,10,18,22,36,43,68,83,119,140,196,235,312,
%T 361,471,550,704,802,1008,1157,1446,1643,2016,2294,2798,3154,3807,
%U 4285,5135,5728,6797,7571,8926,9880,11543,12744,14827,16295,18801,20645
%N Sum of the second largest parts of the partitions of n into 8 squarefree parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/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)^2 * i, where mu is the Möbius function (A008683).
%F a(n) = A326444(n) - A326445(n) - A326446(n) - A326447(n) - A326448(n) - A326449(n) - A326450(n) - A326452(n).
%t Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i * 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]^2, {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]
%Y Cf. A008683, A326443, A326444, A326445, A326446, A326447, A326448, A326449, A326450, A326452.
%K nonn
%O 0,11
%A _Wesley Ivan Hurt_, Jul 06 2019