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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
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OFFSET
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0,5
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COMMENTS
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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:
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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LINKS
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FORMULA
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Let M be 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
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In the array, antidiagonal terms (1, 3, 5, 1) become row 3 of the triangle.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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