This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326444 #7 Jul 06 2019 20:57:45 %S A326444 0,0,0,0,0,0,0,0,8,9,20,22,48,65,112,135,208,255,378,456,640,756,1034, %T A326444 1219,1632,1875,2444,2835,3640,4147,5220,5952,7392,8382,10234,11550, %U A326444 14004,15688,18810,21021,25040,27798,32802,36421,42680,47160,54832,60489 %N A326444 Sum of all the parts in the partitions of n into 8 squarefree parts. %H A326444 <a href="/index/Par#part">Index entries for sequences related to partitions</a> %F A326444 a(n) = 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, where mu is the Möbius function (A008683). %F A326444 a(n) = n * A326443(n). %F A326444 a(n) = A326445(n) + A326446(n) + A326447(n) + A326448(n) + A326449(n) + A326450(n) + A326451(n) + A326452(n). %t A326444 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[n * 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 A326444 Cf. A008683, A326443, A326445, A326446, A326447, A326448, A326449, A326450, A326451, A326452. %K A326444 nonn %O A326444 0,9 %A A326444 _Wesley Ivan Hurt_, Jul 06 2019