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

1,5

Comments

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

Links

Table of n, a(n) for n=1..28.

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, ...].

Example

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.

Sequence in context: A258219 A036560 A308244 * A112973 A162303 A128570

Adjacent sequences: A117294 A117295 A117296 * A117298 A117299 A117300

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 23 2006

Status

approved