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%I #12 Mar 20 2023 15:17:32
%S 0,0,0,0,0,0,0,0,0,0,1,1,2,3,5,7,11,15,22,31,44,58,80,105,140,182,238,
%T 304,393,496,630,787,986,1219,1512,1853,2273,2765,3362,4055,4894,5860,
%U 7016,8351,9931,11746,13885,16330,19188,22452,26242,30549,35531
%N Sum of the ninth largest parts of the partitions of n into 10 parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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)} q.
%F a(n) = A326588(n) - A326589(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326595(n) - A326596(n) - A326597(n) - A326598(n).
%t Table[Total[IntegerPartitions[n,{10}][[;;,9]]],{n,0,60}] (* _Harvey P. Dale_, Mar 18 2023 *)
%Y Cf. A026816, A326588, A326589, A326591, A326592, A326593, A326594, A326595, A326596, A326597, A326598.
%K nonn
%O 0,13
%A _Wesley Ivan Hurt_, Jul 13 2019
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