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%I #5 Dec 26 2023 12:30:09
%S 1,1,1,1,3,1,1,3,6,6,1,3,6,18,16,1,3,6,18,48,44,1,3,6,18,48,132,120,
%T 136,18,48,132,360,328,1,3,6,18,48,132,360,984,896,1,3,6,18,48,132,
%U 360,984,2688,2448,1,3,6,18,48,132,360,984,2688,7344,6688
%N Triangle read by rows, A123191 * (A002605 * (A002605 * 0^(n-k))).
%C Row sums = A002605: (1, 2, 6, 16, 44, 120,...)
%C As a property of eigentriangles, sum of row terms = rightmost term of next row.
%F Triangle read by rows, A123191 * (A002605 * (A002605 * 0^(n-k))). A123191 is
%F unsigned, (A002605 * 0^(n-k))= an infinite lower triangular matrix with
%F A002605 as the main diagonal prefaced with a 1: (1, 1, 2, 6, 16, 44,...)
%F and the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 1, 1;
%e 1, 3, 2;
%e 1, 3, 6, 6;
%e 1, 3, 6, 18, 16;
%e 1, 3, 6, 18, 48, 44;
%e 1, 3, 6, 18, 48, 132, 120;
%e 1, 3, 6, 18, 48, 132, 360, 328;
%e 1, 3, 6, 18, 48, 132, 360, 984, 896;
%e 1, 3, 6, 18, 48, 132, 360, 984, 2688, 2448;
%e 1, 3, 6, 18, 48, 132, 360, 984, 2688, 7344, 6688;
%e ...
%Y Cf. A002605, A123191.
%K nonn,tabl
%O 0,5
%A _Gary W. Adamson_, Feb 14 2009