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A326592 Sum of the seventh largest parts in the partitions of n into 10 parts.

%I A326592 #10 Jul 14 2025 12:22:16
%S A326592 0,0,0,0,0,0,0,0,0,0,1,1,2,3,5,7,11,16,24,34,49,66,92,123,167,220,293,
%T A326592 380,497,636,818,1035,1312,1642,2059,2551,3162,3884,4769,5806,7068,
%U A326592 8539,10310,12370,14826,17670,21038,24920,29482,34725,40848,47852,55989
%N A326592 Sum of the seventh largest parts in the partitions of n into 10 parts.
%H A326592 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326592 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)} o.
%F A326592 a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326593(n) - A326594(n) - A326595(n) - A326596(n) - A326597(n) - A326598(n).
%t A326592 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[o, {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}]
%t A326592 Table[Total[IntegerPartitions[n,{10}][[;;,7]]],{n,0,60}] (* _Harvey P. Dale_, Jul 14 2025 *)
%Y A326592 Cf. A026816, A326588, A326589, A326590, A326591, A326593, A326594, A326595, A326596, A326597, A326598.
%K A326592 nonn
%O A326592 0,13
%A A326592 _Wesley Ivan Hurt_, Jul 13 2019