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%I #11 Mar 30 2012 17:37:36
%S 0,2,3,6,10,18,27,45,65,99,141,206,285,403,549,754,1011,1364,1800,
%T 2388,3116,4072,5257,6791,8678,11093,14058,17800,22380,28111,35087,
%U 43748,54256,67189,82831,101962,124997,153011,186632,227281,275905,334418,404159,487714
%N Total sum of the numbers of partitions with positive k-th ranks of all partitions of n.
%C For the definition of k-th rank see A208478.
%e For n = 4 the partitions of 4 and the four types of ranks of the partitions of 4 are
%e ----------------------------------------------------------
%e Partitions First Second Third Fourth
%e of 4 rank rank rank rank
%e ----------------------------------------------------------
%e 4 4-1 = 3 0-1 = -1 0-1 = -1 0-1 = -1
%e 3+1 3-2 = 1 1-1 = 0 0-1 = -1 0-0 = 0
%e 2+2 2-2 = 0 2-2 = 0 0-0 = 0 0-0 = 0
%e 2+1+1 2-3 = -1 1-1 = 0 1-0 = 1 0-0 = 0
%e 1+1+1+1 1-4 = -3 1-0 = 1 1-0 = 1 1-0 = 1
%e ----------------------------------------------------------
%e 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.
%Y Row sums of A208478.
%Y Cf. A208482, A208483.
%K nonn
%O 1,2
%A _Omar E. Pol_, Mar 07 2012
%E More terms from _Alois P. Heinz_, Mar 11 2012