%I #6 Apr 18 2013 11:30:24
%S 1,0,1,0,1,1,0,2,2,2,0,6,5,6,6,0,24,16,18,24,23,0,120,64,62,84,115,
%T 105,0,720,312,252,312,460,630,550,0,5040,1812,1212,1302,1840,2835,
%U 3850,3236,0,40320,12288,6856,6240,7935,12180,19250,25888,21127
%N Triangle read by rows, A084938 * A165489 diagonalized as an infinite lower triangular matrix.
%C A165490 is an eigentriangle (triangle A084938 * its shifted eigensequence), having two distinct properties: row sums = A165489, the eigensequence of triangle A084938: (1, 1, 2, 6, 23, 105, 550, 3236,...), and sum of row terms = rightmost term of next row.
%F Triangle read by rows, A084938 * its shifted eigensequence (1, 1, 1, 2, 6, 23,...) diagonalized as an infinite lower triangular matrix:
%F 1;
%F 0, 1;
%F 0, 0, 1;
%F 0, 0, 0, 2;
%F 0, 0, 0, 0, 6;
%F 0, 0, 0, 0, 0, 23;
%F ...
%e First few rows of the triangle =
%e 1;
%e 0, 1;
%e 0, 1, 1;
%e 0, 2, 2, 2;
%e 0, 6, 5, 6, 6;
%e 0, 24, 16, 18, 24, 23;
%e 0, 120, 64, 62, 84, 115, 105;
%e 0, 720, 312, 252, 312, 460, 630, 550;
%e 0, 5040, 1812, 1212, 1302, 1840, 2835, 3850, 3236;
%e 0, 40320, 12288, 6856, 6240, 7935, 12180, 19250, 25888, 21127;
%e ...
%e Example: row 4 = (0, 6, 5, 6, 6) = termwise products of (0, 6, 5, 3, 1) and (1, 1, 1, 2, 6); where (0, 6, 5, 3, 1) = row 4 of triangle A084938.
%Y Cf. A084938, A165489.
%K nonn,tabl
%O 0,8
%A _Gary W. Adamson_, Sep 20 2009