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A153206 Convolution triangle by rows, T(n,k) = A153197(n-k) * A153198.

%I A153206 #4 Jun 02 2025 01:16:18
%S A153206 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 A153206 143,748,189,102,75,70,86,143,509,3128,748,378,255,210,215,286,509,
%U A153206 1922,13731,3128,1496,945,714,645,715,1018,1922,7651
%N A153206 Convolution triangle by rows, T(n,k) = A153197(n-k) * A153198.
%C A153206 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 A153206 Right border = A006789, row sums = A006789 shifted.
%F A153206 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 A153206 First few rows of the triangle =
%e A153206 1;
%e A153206 1, 1;
%e A153206 2, 1, 2;
%e A153206 5, 2, 2, 5;
%e A153206 15, 5, 4, 5, 14;
%e A153206 51, 15, 10, 10, 14, 43;
%e A153206 189, 51, 30, 25, 28, 43, 143;
%e A153206 748, 189, 102, 75, 70, 86, 143, 509;
%e A153206 3128, 748, 378, 255, 210, 215, 286, 509, 1922;
%e A153206 13731, 3128, 1496, 945, 714, 645, 715, 1018, 1922, 7651;
%e A153206 62969, 13731, 6256, 3740, 2646, 2193, 2145, 2545, 3844, 7651, 31965;
%e A153206 ...
%e A153206 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 A153206 Cf. A006789, A153197
%K A153206 nonn,tabl
%O A153206 0,4
%A A153206 _Gary W. Adamson_, Dec 20 2008