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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 (list; table; graph; refs; listen; history; text; internal format)
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 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

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Last modified October 26 05:15 EDT 2020. Contains 338027 sequences. (Running on oeis4.)