A208479 Total sum of the numbers of partitions with positive k-th ranks of all partitions of n.

0, 2, 3, 6, 10, 18, 27, 45, 65, 99, 141, 206, 285, 403, 549, 754, 1011, 1364, 1800, 2388, 3116, 4072, 5257, 6791, 8678, 11093, 14058, 17800, 22380, 28111, 35087, 43748, 54256, 67189, 82831, 101962, 124997, 153011, 186632, 227281, 275905, 334418, 404159, 487714

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 number of partitions of 4 with positive k-th ranks are 2, 1, 2, 1 so the total sum is a(4) = 2+1+2+1 = 6.
		

Crossrefs

Row sums of A208478.

Cf. A208482, A208483.

Extensions

More terms from Alois P. Heinz, Mar 11 2012