1,5

The operation used in generating the triangle is analogous to the binomial transform operation used in generating triangle A058127.

Let a(1) = 1, then n-th row is generated by performing the operation (M * V) on the (n-1)-th row and extracting the first n terms. M = the Narayana triangle of A001263 considered as a transform. V = the (n-1)-th row of the triangle as a Vector, V; followed by zeros: [a, b, c, 0, 0, 0...].

4-th row = (1, 3, 11, 37), the first four terms of M * V = (1, 3, 11, 37, 101, 231, 463,...); where M = the Narayana triangle as an infinitely lower triangular matrix, and V = the Vector formed by row 3: [1, 2, 4, 0, 0, 0...].

First few rows of the triangle are:

1;

1, 1;

1, 2, 4;

1, 3, 11, 37;

1, 4, 21, 122, 621;

1, 5, 34, 273, 2302, 16526;

...

Cf. A001263, A058127.

Sequence in context: A121426 A004515 A036560 this_sequence A112973 A128570 A011167

Adjacent sequences: A117294 A117295 A117296 this_sequence A117298 A117299 A117300

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2006