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A125231
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Triangle read by rows: T(n,k) = ceiling((k+1)/2)*binomial(n,k) (0 <= k <= n).
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1
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1, 1, 1, 1, 2, 2, 1, 3, 6, 2, 1, 4, 12, 8, 3, 1, 5, 20, 20, 15, 3, 1, 6, 30, 40, 45, 18, 4, 1, 7, 42, 70, 105, 63, 28, 4, 1, 8, 56, 112, 210, 168, 112, 32, 5, 1, 9, 72, 168, 378, 378, 336, 144, 45, 5, 1, 10, 90, 240, 630, 756, 840, 480, 225, 50, 6, 1, 11, 110, 330, 990, 1386, 1848
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OFFSET
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0,5
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COMMENTS
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Row sums = A045623: (1, 2, 5, 12, 28, 64, 144, 320, ...).
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LINKS
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EXAMPLE
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First few rows of the triangle:
1;
1, 1;
1, 2, 2;
1, 3, 6, 2;
1, 4, 12, 8, 3;
1, 5, 20, 20, 15, 3;
1, 6, 30, 40, 45, 18, 4;
1, 7, 42, 70, 105, 63, 28, 4;
...
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MAPLE
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T:=(n, k)->ceil((k+1)/2)*binomial(n, k): for n from 0 to 12 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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MATHEMATICA
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Flatten[Table[Ceiling[(k+1)/2]Binomial[n, k], {n, 0, 20}, {k, 0, n}]] (* Harvey P. Dale, Aug 31 2015 *)
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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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