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A326472
Sum of the second largest parts of the partitions of n into 9 parts.
9
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 27, 39, 63, 91, 135, 188, 272, 368, 510, 682, 918, 1201, 1586, 2039, 2639, 3354, 4264, 5346, 6716, 8319, 10312, 12657, 15516, 18858, 22908, 27599, 33226, 39740, 47449, 56338, 66809, 78792, 92799, 108810, 127365
OFFSET
0,12
FORMULA
a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} i.
a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326471(n) - A326473(n).
MATHEMATICA
Table[Total[IntegerPartitions[n, {9}][[;; , 2]]], {n, 0, 50}] (* _Harvey P. Dale_, Dec 03 2023 *)
KEYWORD
nonn
AUTHOR
_Wesley Ivan Hurt_, Jul 10 2019
STATUS
approved