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A117297
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Triangle read by rows generated from the Narayana transform.
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0
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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; internal format)
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OFFSET
| 1,5
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COMMENTS
| The operation used in generating the triangle is analogous to the binomial transform operation used in generating triangle A058127.
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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...].
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EXAMPLE
| 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;
...
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CROSSREFS
| Cf. A001263, A058127.
Sequence in context: A190183 A004515 A036560 * A112973 A162303 A128570
Adjacent sequences: A117294 A117295 A117296 * A117298 A117299 A117300
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2006
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