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A210952 Triangle read by rows: T(n,k) = sum of all parts of the k-th column of the partitions of n but with the partitions aligned to the right margin.

%I A210952 #29 Jun 01 2012 19:17:09
%S A210952 1,1,3,1,3,5,1,3,7,9,1,3,7,12,12,1,3,7,14,21,20,1,3,7,14,24,31,25,1,3,
%T A210952 7,14,26,40,47,38,1,3,7,14,26,43,61,66,49,1,3,7,14,26,45,70,92,93,69,
%U A210952 1,3,7,14,26,45,73,106,130,124,87,1,3,7,14
%N A210952 Triangle read by rows: T(n,k) = sum of all parts of the k-th column of the partitions of n but with the partitions aligned to the right margin.
%F A210952 T(n,k) = Sum_{j=1..n} A210953(j,k). - _Omar E. Pol_, May 26 2012
%e A210952 For n = 6 the illustration shows the partitions of 6 aligned to the right margin and below the sums of the columns:
%e A210952 .
%e A210952 .                      6
%e A210952 .                  3 + 3
%e A210952 .                  4 + 2
%e A210952 .              2 + 2 + 2
%e A210952 .                  5 + 1
%e A210952 .              3 + 2 + 1
%e A210952 .              4 + 1 + 1
%e A210952 .          2 + 2 + 1 + 1
%e A210952 .          3 + 1 + 1 + 1
%e A210952 .      2 + 1 + 1 + 1 + 1
%e A210952 .  1 + 1 + 1 + 1 + 1 + 1
%e A210952 -------------------------
%e A210952 .  1,  3,  7, 14, 21, 20
%e A210952 .
%e A210952 So row 6 lists 1, 3, 7, 14, 21, 20.
%e A210952 Triangle begins:
%e A210952 1;
%e A210952 1, 3;
%e A210952 1, 3, 5;
%e A210952 1, 3, 7,  9;
%e A210952 1, 3, 7, 12, 12;
%e A210952 1, 3, 7, 14, 21, 20;
%e A210952 1, 3, 7, 14, 24, 31, 25;
%e A210952 1, 3, 7, 14, 26, 40, 47, 38;
%e A210952 1, 3, 7, 14, 26, 43, 61, 66, 49;
%e A210952 1, 3, 7, 14, 26, 45, 70, 92, 93, 69:
%Y A210952 Mirror of triangle A206283. Rows sums give A066186. Rows converge to A014153. Right border gives A046746, >= 1.
%Y A210952 Cf. A135010, A138121, A181187, A210763, A210950, A210951, A210953, A210961, A210970.
%K A210952 nonn,tabl
%O A210952 1,3
%A A210952 _Omar E. Pol_, Apr 22 2012