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A099233
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Square array read by antidiagonals associated to sections of 1/(1-x-x^k).
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7
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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 6, 5, 1, 1, 1, 5, 10, 13, 8, 1, 1, 1, 6, 15, 26, 28, 13, 1, 1, 1, 7, 21, 45, 69, 60, 21, 1, 1, 1, 8, 28, 71, 140, 181, 129, 34, 1, 1, 1, 9, 36, 105, 251, 431, 476, 277, 55, 1, 1, 1, 10, 45, 148, 413, 882, 1326, 1252, 595, 89, 1
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OFFSET
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0,9
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LINKS
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FORMULA
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Square array T(n, k) = Sum_{j=0..n} binomial(k(n-j), j).
Rows are generated by 1/(1-x(1+x)^k) and satisfy a(n) = Sum_{k=0..n} binomial(n, k)a(n-k-1).
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EXAMPLE
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Rows begin
1, 1, 1, 1, 1, 1, ...
1, 1, 2, 3, 5, 8, ...
1, 1, 3, 6, 13, 28, ...
1, 1, 4, 10, 26, 69, ...
1, 1, 5, 15, 45, 140, ...
Row 1 is the 0-section of 1/(1-x-x) (A000079);
Row 2 is the 1-section of 1/(1-x-x^2) (A000045);
Row 3 is the 2-section of 1/(1-x-x^3) (A000930);
Row 4 is the 3-section of 1/(1-x-x^4) (A003269);
etc.
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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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