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A326590
Sum of the ninth largest parts of the partitions of n into 10 parts.
10
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, 304, 393, 496, 630, 787, 986, 1219, 1512, 1853, 2273, 2765, 3362, 4055, 4894, 5860, 7016, 8351, 9931, 11746, 13885, 16330, 19188, 22452, 26242, 30549, 35531
OFFSET
0,13
FORMULA
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.
a(n) = A326588(n) - A326589(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326595(n) - A326596(n) - A326597(n) - A326598(n).
MATHEMATICA
Table[Total[IntegerPartitions[n, {10}][[;; , 9]]], {n, 0, 60}] (* Harvey P. Dale, Mar 18 2023 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 13 2019
STATUS
approved