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A102462
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Max{ k!/(a(1)!*a(2)!*..*a(n)!) : a(1)+2*a(2)+3*a(3)+..+n*a(n) = n, a(1)+a(2)+..+a(n) = k }.
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7
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1, 1, 1, 2, 3, 4, 6, 12, 20, 30, 60, 105, 168, 280, 504, 840, 1512, 2520, 5040, 9240, 15840, 27720, 55440, 102960, 180180, 360360, 675675, 1201200, 2162160, 4084080, 7351344, 12697776, 24504480, 46558512, 84651840, 155195040, 296281440, 543182640, 961015440
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OFFSET
| 0,4
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COMMENTS
| a(n) is the greatest number in row n of A048996 and in row n of A072811. Thus a(n) is the greatest number of compositions (permutations) obtainable from some partition of n. Example: a(7)=12 is the greatest number of compositions from some partition of 7, specifically, the partition {3,2,1,1}. - Clark Kimberling, Dec 24 2006
The partition(s) giving this optimum is always one where #{parts equal to i} >= #{parts equal to j} if i <= j. These partitions are counted in A007294. - Franklin T. Adams-Watters, Apr 08 2008
The number of partition(s) giving this optimum is given by A198254. - Olivier Gerard, Nov 17 2011
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..100
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CROSSREFS
| Cf. A059171, A102356, A048992, A072811.
Sequence in context: A118651 A129297 A018343 * A018369 A078495 A161701
Adjacent sequences: A102459 A102460 A102461 * A102463 A102464 A102465
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 23 2005
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