

A117297


Triangle read by rows generated from the Narayana transform.


0



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
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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 nth row is generated by performing the operation (M * V) on the (n1)th row and extracting the first n terms. M = the Narayana triangle of A001263 considered as a transform. V = the (n1)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 are:
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



