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A208483
Total sum of the sums of all positive k-th ranks of all partitions of n.
7
0, 2, 4, 8, 14, 26, 40, 68, 100, 156, 224, 334, 466, 668, 920, 1278, 1726, 2356, 3130, 4190, 5508, 7254, 9422, 12268, 15764, 20284, 25852, 32934, 41616, 52578, 65938, 82648, 102976, 128144, 158660, 196222, 241534, 296946, 363632, 444650, 541794, 659268, 799606
OFFSET
1,2
COMMENTS
For the definition of k-th rank see A208478.
EXAMPLE
For n = 4 the partitions of 4 and the four types of ranks of the partitions of 4 are
----------------------------------------------------------
Partitions First Second Third Fourth
of 4 rank rank rank rank
----------------------------------------------------------
4 4-1 = 3 0-1 = -1 0-1 = -1 0-1 = -1
3+1 3-2 = 1 1-1 = 0 0-1 = -1 0-0 = 0
2+2 2-2 = 0 2-2 = 0 0-0 = 0 0-0 = 0
2+1+1 2-3 = -1 1-1 = 0 1-0 = 1 0-0 = 0
1+1+1+1 1-4 = -3 1-0 = 1 1-0 = 1 1-0 = 1
----------------------------------------------------------
The sums of positive k-th ranks of the partitions of 4 are 4, 1, 2, 1 so the total sum is a(4) = 4+1+2+1 = 8.
CROSSREFS
Row sums of triangle A208482.
Sequence in context: A164148 A065492 A298880 * A284735 A006777 A036609
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 07 2012
EXTENSIONS
More terms from Alois P. Heinz, Mar 11 2012
STATUS
approved