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A353594
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Triangle read by rows, T(n, k) = Sum_{j=0..n} binomial(j, k)*A352687(n, j).
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0
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1, 1, 1, 2, 3, 1, 4, 8, 5, 1, 10, 25, 22, 8, 1, 28, 84, 95, 50, 12, 1, 84, 294, 406, 280, 100, 17, 1, 264, 1056, 1722, 1470, 700, 182, 23, 1, 858, 3861, 7260, 7392, 4410, 1554, 308, 30, 1, 2860, 14300, 30459, 36036, 25872, 11550, 3150, 492, 38, 1
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graph;
refs;
listen;
history;
text;
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OFFSET
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0,4
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LINKS
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EXAMPLE
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Triangle starts:
[0] 1;
[1] 1, 1;
[2] 2, 3, 1;
[3] 4, 8, 5, 1;
[4] 10, 25, 22, 8, 1;
[5] 28, 84, 95, 50, 12, 1;
[6] 84, 294, 406, 280, 100, 17, 1;
[7] 264, 1056, 1722, 1470, 700, 182, 23, 1;
[8] 858, 3861, 7260, 7392, 4410, 1554, 308, 30, 1;
[9] 2860, 14300, 30459, 36036, 25872, 11550, 3150, 492, 38, 1;
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MAPLE
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S := (n, k) -> if n = k then 1 elif k = 0 then 0 else
binomial(n, k)^2*(k*(2*k^2 + (n + 1)*(n - 2*k)))/(n^2*(n - 1)*(n - k + 1)) fi:
T := (n, k) -> add(binomial(j, k)*S(n, j), j = 0..n):
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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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