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Convolution triangle by rows, T(n,k) = A153197(n-k) * A153198
1

%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