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A093430
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Triangle read by rows: T(n,k) = lcm(n, n-1, ..., n-k+2, n-k+1)/lcm(1, 2, ..., k) (1 <= k <= n).
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3
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1, 2, 1, 3, 3, 1, 4, 6, 2, 1, 5, 10, 10, 5, 1, 6, 15, 10, 5, 1, 1, 7, 21, 35, 35, 7, 7, 1, 8, 28, 28, 70, 14, 14, 2, 1, 9, 36, 84, 42, 42, 42, 6, 3, 1, 10, 45, 60, 210, 42, 42, 6, 3, 1, 1, 11, 55, 165, 330, 462, 462, 66, 33, 11, 11, 1, 12, 66, 110, 165, 66, 462, 66, 33, 11, 11, 1, 1, 13
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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T(7,3) = lcm(7,6,5)/lcm(1,2,3) = 210/6 = 35.
Triangle starts:
1;
2, 1;
3, 3, 1;
4, 6, 2, 1;
5, 10, 10, 5, 1;
6, 15, 10, 5, 1, 1;
...
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MAPLE
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T:=(n, k)->lcm(seq(i, i=n-k+1..n))/lcm(seq(j, j=1..k)): for n from 1 to 13 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form # Emeric Deutsch, Jan 30 2006
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MATHEMATICA
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t[n_, k_] := LCM @@ Table[j, {j, n-k+1, n}] / LCM @@ Table[j, {j, 1, k}]; t[_, 0] = 1; Table[t[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 23 2014 *)
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CROSSREFS
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Cf. A067049 (same triangle with an additional leading column of ones).
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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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