%I #12 Nov 21 2023 00:34:32

%S 0,0,0,0,0,0,0,0,0,0,1,1,3,5,10,15,27,39,63,91,137,190,277,376,525,

%T 704,956,1255,1671,2160,2818,3599,4616,5819,7369,9187,11480,14179,

%U 17527,21441,26256,31851,38649,46543,56022,66980,80050,95083,112860,133266

%N Sum of the second 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)} i.

%F a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326595(n) - A326596(n) - A326598(n).

%t Table[Total[IntegerPartitions[n,{10}][[;;,2]]],{n,0,50}] (* _Harvey P. Dale_, Nov 19 2023 *)

%Y Cf. A026816, A326588, A326589, A326590, A326591, A326592, A326593, A326594, A326595, A326596, A326598.

%K nonn

%O 0,13

%A _Wesley Ivan Hurt_, Jul 13 2019