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A144480
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T(n,k) = binomial(n, k)*min(k + 1, n - k + 1), triangle read by rows (n >= 0, 0 <= k <= n).
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1
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1, 1, 1, 1, 4, 1, 1, 6, 6, 1, 1, 8, 18, 8, 1, 1, 10, 30, 30, 10, 1, 1, 12, 45, 80, 45, 12, 1, 1, 14, 63, 140, 140, 63, 14, 1, 1, 16, 84, 224, 350, 224, 84, 16, 1, 1, 18, 108, 336, 630, 630, 336, 108, 18, 1, 1, 20, 135, 480, 1050, 1512, 1050, 480, 135, 20, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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If k <= floor(n/2), then T(n,k) = binomial(n, k)*(k + 1), otherwise T(n,k) = binomial(n, k)*(n - k - 1).
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 4, 1;
1, 6, 6, 1;
1, 8, 18, 8, 1;
1, 10, 30, 30, 10, 1;
1, 12, 45, 80, 45, 12, 1;
1, 14, 63, 140, 140, 63, 14, 1;
1, 16, 84, 224, 350, 224, 84, 16, 1;
1, 18, 108, 336, 630, 630, 336, 108, 18, 1;
1, 20, 135, 480, 1050, 1512, 1050, 480, 135, 20, 1;
...
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MATHEMATICA
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Table[Table[Binomial[n, m]*If[m <= Floor[n/2], 1 + m, 1 + n - m], {m, 0, n}], {n, 0, 10}] // Flatten
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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