[seqfan] Summing ranks of partitions in A105805/7

[Lang, Wolfdieter]

Dear Richard and  seqfans,

MEA CULPA!

1) I also cannot reproduce the numbers in A105807. When I use my list of partitions for n=1 .. 25 in Abramowitz-Stegun (A-St) order I also find Richard 's list for n=1..25. 
I suspect that I used in the old calculation a not correctly  A-St ordered list. In fact, in the link in A105805 the list of ranks for n=11 ..15 is also not in A-St order. 
I will send a corrected version of this link to OEIS.

2) I have compared Richard's Maple programs AScompare (a line  'local i:' could be added) and AsPrts given in A119441 (and in A105805) with my rank Maple program using my A-St ordered list of partitions for n=1..25. These 9295 partitions agree.

3) However, the sequence A105807 is not meaningful (not interesting)! It should be discarded (recycled). 
The reason I proposed this sequence was based on the wrong assumption that the rows in A105805  were antisymmetric in sign due to conjugacy. 
But Franklin T. Adams-Watters, in Jan 17 2006, already corrected my mistake (but I was not aware of this correction). 
Thus the intended meaningful sequence is:  Sum of positive ranks of the partitions of n, n>=1. Sum the absolute value of the ranks in each row and divide by 2.  
This sequence is in fact already in OEIS as A209616 thanks to Omar E. Pol, Mar 10 2012. 
My first 25 entries are [0, 1, 2, 4, 7, 12, 18, 29, 42, 63, 89, 128, 176, 246, 333, 453, 603, 807, 1058, 1393, 1807, 2346, 3011, 3867, 4915] which agree with A209616.

Conclusion: I am very sorry for these mistakes. I will suggest to recycle A105807, add a reference to A209616 in A105805,  
and send a revised version of the link to A105805.

Best regards,
Wolfdieter