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

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

Offset

0,4

Comments

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.

Links

Table of n, a(n) for n=0..54.

Formula

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.

Example

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,...).

Crossrefs

Cf. A006789, A153197

Sequence in context: A230219 A147292 A078391 * A144155 A109631 A361399

Adjacent sequences: A153203 A153204 A153205 * A153207 A153208 A153209

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 20 2008

Status

approved