cp's OEIS Frontend

A326632 Sum of the sixth largest parts of the partitions of n into 10 squarefree parts.

%I A326632 #10 Jul 14 2019 21:10:12
%S A326632 0,0,0,0,0,0,0,0,0,0,1,1,2,2,4,5,9,11,16,21,31,37,51,61,83,99,129,150,
%T A326632 197,229,288,332,417,479,589,676,830,950,1150,1310,1588,1802,2148,
%U A326632 2431,2897,3264,3843,4322,5067,5684,6604,7380,8557,9538,10961,12198
%N A326632 Sum of the sixth largest parts of the partitions of n into 10 squarefree parts.
%H A326632 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326632 a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} mu(r)^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-r)^2 * m, where mu is the Möbius function (A008683).
%F A326632 a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326631(n) - A326633(n) - A326634(n) - A326635(n) - A326636(n) - A326637(n).
%t A326632 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[m * MoebiusMu[r]^2 * 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 - r]^2 , {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 50}]
%Y A326632 Cf. A008683, A326626, A326627, A326628, A326629, A326630, A326631, A326633, A326634, A326635, A326636, A326637.
%K A326632 nonn
%O A326632 0,13
%A A326632 _Wesley Ivan Hurt_, Jul 14 2019