%I A137683
%S A137683 1,0,1,3,2,1,1,4,3,1,5,3,6,4,1,5,5,9,10,5,1,11,6,16,20,15,6,1,10,12,23,
%T A137683 36,35,21,7,1,20,5,27,55,70,56,28,8,1,24,11,31,81,125,126,84,36,9,1,38,
%U A137683 9,51,123,211,252,210,120,45,10,1
%V A137683 1,0,1,3,-2,1,1,4,-3,1,5,-3,6,-4,1,5,5,-9,10,-5,1,11,-6,16,-20,15,-6,1,
               10,12,-23,36,
%W A137683 -35,21,-7,1,20,-5,27,-55,70,-56,28,-8,1,24,11,-31,81,-125,126,-84,36,
               -9,1,38,-9,51,
%X A137683 -123,211,-252,210,-120,45,-10,1
%N A137683 Triangle read by rows, A026794 * A007318^(-1).
%C A137683 Row sums = the partition numbers, A000041: (1, 1, 2, 3, 5, 7, 11, 15, 
               22,...).
%F A137683 As an infinite lower triangular matrix, A026794 * the inverse of Pascal's 
               triangle.
%e A137683 First few rows of the triangle are:
%e A137683 1;
%e A137683 0, 1;
%e A137683 3, -2, 1;
%e A137683 1, 4, -3, 1;
%e A137683 5, -3, 6, -4, 1;
%e A137683 5, 5, -9, 10, -5, 1;
%e A137683 ...
%e A137683 T(3,1) = -3 = (0, 0, 1, -3) dot (3, 1, 0, 1) = (0, 0, 0, -3)
%Y A137683 Cf. A000041, A026794.
%Y A137683 Sequence in context: A143772 A053989 A097794 this_sequence A046225 A123396 
               A058280
%Y A137683 Adjacent sequences: A137680 A137681 A137682 this_sequence A137684 A137685 
               A137686
%K A137683 tabl,sign
%O A137683 0,4
%A A137683 Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 05 2008