A117297 Triangle read by rows generated from the Narayana transform.

1, 1, 1, 1, 2, 4, 1, 3, 11, 37, 1, 4, 21, 122, 621, 1, 5, 34, 273, 2302, 16526, 1, 6, 50, 508, 2763, 66482, 640207

Offset: 1

Author

Gary W. Adamson, Apr 23 2006

Keywords

• nonn
• tabl

Comments

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

Examples

			4th 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:
  1;
  1, 1;
  1, 2,  4;
  1, 3, 11,  37;
  1, 4, 21, 122,  621;
  1, 5, 34, 273, 2302, 16526;
  ...
		

Crossrefs

Cf. A001263, A058127.

Formula

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, ...].