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A208483 Total sum of the sums of all positive k-th ranks of all partitions of n. 7

%I

%S 0,2,4,8,14,26,40,68,100,156,224,334,466,668,920,1278,1726,2356,3130,

%T 4190,5508,7254,9422,12268,15764,20284,25852,32934,41616,52578,65938,

%U 82648,102976,128144,158660,196222,241534,296946,363632,444650,541794,659268,799606

%N Total sum of the sums of all 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 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.

%Y Row sums of triangle A208482.

%Y Cf. A208478, A208479.

%K nonn

%O 1,2

%A _Omar E. Pol_, Mar 07 2012

%E More terms from _Alois P. Heinz_, Mar 11 2012

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Last modified January 21 03:58 EST 2022. Contains 350473 sequences. (Running on oeis4.)