cp's OEIS Frontend

A326532 Sum of the largest parts of the partitions of n into 9 squarefree parts.

%I A326532 #5 Jul 12 2019 07:19:44
%S A326532 0,0,0,0,0,0,0,0,0,1,2,5,5,13,19,34,40,60,82,124,150,216,267,371,443,
%T A326532 595,706,941,1090,1423,1656,2110,2415,3026,3485,4286,4876,5937,6749,
%U A326532 8131,9145,10932,12308,14580,16302,19190,21446,25053,27865,32372,36004
%N A326532 Sum of the largest parts of the partitions of n into 9 squarefree parts.
%H A326532 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326532 a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/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)^2 * (n-i-j-k-l-m-o-p-q), where mu is the Möbius function (A008683).
%F A326532 a(n) = A326523(n) - A326524(n) - A326525(n) - A326526(n) - A326527(n) - A326528(n) - A326529(n) - A326530(n) - A326531(n).
%t A326532 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(n-i-j-k-l-m-o-p-q) * 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]^2, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 80}]
%Y A326532 Cf. A008683, A326522, A326523, A326524, A326525, A326526, A326527, A326528, A326529, A326530, A326531.
%K A326532 nonn
%O A326532 0,11
%A A326532 _Wesley Ivan Hurt_, Jul 11 2019