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A112338
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Triangle read by rows, generated from A001263.
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1
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1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 12, 14, 1, 1, 5, 22, 57, 42, 1, 1, 6, 35, 148, 303, 132, 1, 1, 7, 51, 305, 1144, 1743, 429, 1, 8, 70, 546, 3105, 9784, 10629, 1430, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Rows of the array are row sums of n-th powers of the Narayana triangle; e.g. row 1 = A000108: (1, 2, 5, 14, 42...); row 2 = row sums of the Narayana triangle squared (A103370): (1, 3, 12, 57, 303...), etc.
First few rows of the array are:
1, 1, 1, 1, 1, 1,...
1, 2, 5, 14, 42, 132,...
1, 3, 12, 57, 303, 1743,...
1, 4, 22, 148, 1144, 9784,...
1, 5, 35, 305, 3105, 35505,...
First few rows of the triangle are:
1;
1, 1;
1, 2, 1;
1, 3, 5, 1;
1, 4, 12, 14, 1;
1, 5, 22, 57, 42, 1;
1, 6, 35, 148, 303, 132, 1;
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FORMULA
| Let M = the infinite lower triangular Narayana triangle (A001263). Perform M^n * [1 0 0 0...] getting an array. Take antidiagonals of the array which become rows of the triangle A112338.
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EXAMPLE
| In the array, antidiagonal terms (1, 3, 5, 1) become row 3 of the triangle.
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CROSSREFS
| Cf. A001263, A000326, A005915, A095266, A000108, A103370.
Sequence in context: A094954 A083064 A204057 * A111672 A128198 A123349
Adjacent sequences: A112335 A112336 A112337 * A112339 A112340 A112341
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 04 2005
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