0,4

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,...).

Right border = A006789, row sums = A006789 shifted.

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.

First few rows of the triangle =

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, 143;

748, 189, 102, 75, 70, 86, 143, 509;

3128, 748, 378, 255, 210, 215, 286, 509, 1922;

13731, 3128, 1496, 945, 714, 645, 715, 1018, 1922, 7651;

62969, 13731, 6256, 3740, 2646, 2193, 2145, 2545, 3844, 7651, 31965;

...

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,...).

Cf. A006789, A153197

Sequence in context: A057031 A147292 A078391 this_sequence A144155 A109631 A095149

Adjacent sequences: A153203 A153204 A153205 this_sequence A153207 A153208 A153209

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 20 2008