%I
%S 1,2,1,4,2,3,8,4,6,9,16,8,12,18,27,32,16,24,36,54,81,64,32,48,72,108,
%T 162,243,128,64,96,144,216,324,486,729,256,128,192,288,432,648,972,
%U 1458,2187,512,256,384,576,864,1296,1944,2916,4374,6561
%N Eigentriangle by rows, T(n,k) = A000079(nk) * (diagonalized matrix of (1,1,3,9,27,81,...)).
%C Row sums = 3^n
%C Sum of nth row terms = rightmost term of next row.
%C Eigensequence of the triangle = A153280: (1, 3, 15, 165, 4785, 397155,...)
%F Triangle read by rows, M*Q. M = triangle T(n,k) = A000079(nk); powers of 2 in every column. Q = an infinite lower triangular matrix with powers of 3 prefaced with a 1: (1,1,3,9,27,...) as the main diagonal and the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 2, 1;
%e 4, 2, 3;
%e 8, 4, 6, 9;
%e 16, 8, 12, 18, 27;
%e 32, 16, 24, 36, 54, 81;
%e 64, 32, 48, 72, 108, 162, 243;
%e 128, 64, 96, 144, 216, 324, 486, 729;
%e 256, 128, 192, 288, 432, 648, 972, 1458, 2187;
%e 512, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561;
%e ...
%e Row 3 = (8, 4, 6, 9) = termwise products of (8, 4, 2, 1) and (1, 1, 3, 9).
%Y Cf. A000079, A000244, A153280
%K nonn,tabl
%O 0,2
%A _Gary W. Adamson_, Dec 23 2008
