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%I #5 Apr 18 2013 11:16:08
%S 1,1,1,3,1,2,9,3,2,6,29,9,6,6,20,97,29,18,18,20,70,333,97,58,54,60,70,
%T 252,1165,333,194,174,180,210,252,924,4135,1165,666,582,580,630,756,
%U 924,3432,14845,4135,2330,1998,1940,2030,2268,2772,3432,12870
%N Eigentriangle, row sums = A000984
%C Row sums = A000984: (1, 2, 6, 20, 70, 252,...), left border = A081696.
%C Sum of n-th row terms = rightmost term of next row.
%F Triangle read by rows, M*Q. M = an infinite lower triangular matrix with A081696: (1, 1, 3, 9, 29, 97, 333, 1165,...) in every column; and Q = a matrix with A000984 as the main diagonal (prefaced with a 1): (1, 1, 2, 6, 20, 70, 252,...) and the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 1, 1;
%e 3, 1, 2;
%e 9, 3, 2, 6;
%e 29, 9, 6, 6, 20;
%e 97, 29, 18, 18, 20, 70;
%e 333, 97, 58, 54, 60, 70, 252;
%e 1165, 333, 194, 174, 180, 210, 252, 924;
%e 4135, 1165, 666, 582, 580, 630, 756, 924, 3432;
%e 14845, 4135, 2330, 1998, 1940, 2030, 2268, 2772, 3432, 12870;
%e ...
%e Row 3 = (9, 3, 2, 6) = termwise products of (9, 3, 1, 1) and (1, 1, 2, 6).
%Y Cf. A000984, A081696.
%K nonn,tabl
%O 0,4
%A _Gary W. Adamson_, Nov 29 2008
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