%I #2 Mar 30 2012 17:25:33
%S 1,1,1,2,1,2,5,2,2,5,15,5,4,5,14,51,15,10,10,14,43,189,51,30,25,28,43,
%T 143,748,189,102,75,70,86,143,509,3128,748,378,255,210,215,286,509,
%U 1922,13731,3128,1496,945,714,645,715,1018,1922,7651
%N Convolution triangle by rows, T(n,k) = A153197(n-k) * A153198
%C A153197 prefaced with a 1: (1, 1, 2, 5, 15, 51,...) convolved with A006789 (1, 1, 2, 5, 14, 43,...) = A006789 shifted: (1, 2, 5, 14, 43, 143,...).
%C Right border = A006789, row sums = A006789 shifted.
%F Convolution triangle by rows, T(n,k) = A153197(n-k) * A153198 = a * b, where a = an infinite lower triangular matrix with A153197 prefaced with a 1: (1, 1, 2, 5, 15, 51, 189, 748,...) in every column; and b = an infinite lower triangular matrix with A006789 in the main diagonal and the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 1, 1;
%e 2, 1, 2;
%e 5, 2, 2, 5;
%e 15, 5, 4, 5, 14;
%e 51, 15, 10, 10, 14, 43;
%e 189, 51, 30, 25, 28, 43, 143;
%e 748, 189, 102, 75, 70, 86, 143, 509;
%e 3128, 748, 378, 255, 210, 215, 286, 509, 1922;
%e 13731, 3128, 1496, 945, 714, 645, 715, 1018, 1922, 7651;
%e 62969, 13731, 6256, 3740, 2646, 2193, 2145, 2545, 3844, 7651, 31965;
%e ...
%e Row 5 = (51, 15, 10, 10, 14, 43), = termwise products of (51, 15, 5, 2, 1, 1) and (1, 1, 2, 5, 14, 43), where A153197 = (1, 2, 5, 15, 51,...); and A006789 = (1, 1, 2, 5, 14, 43,...).
%Y Cf. A006789, A153197
%K nonn,tabl
%O 0,4
%A _Gary W. Adamson_, Dec 20 2008