A208483 Total sum of the sums of all positive k-th ranks of all partitions of n.

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

Author

Omar E. Pol, Mar 07 2012

Keywords

• nonn

Comments

For the definition of k-th rank see A208478.

Examples

			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.

Cf. A208478, A208479.

Extensions

More terms from Alois P. Heinz, Mar 11 2012