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A078760
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Combinations of a partition: number of ways to label a partition (of size n) with numbers 1 to n.
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2
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1, 1, 1, 2, 1, 3, 6, 1, 4, 6, 12, 24, 1, 5, 10, 20, 30, 60, 120, 1, 6, 15, 30, 20, 60, 120, 90, 180, 360, 720, 1, 7, 21, 42, 35, 105, 210, 140, 210, 420, 840, 630, 1260, 2520, 5040, 1, 8, 28, 56, 56, 168, 336, 70, 280, 420, 840, 1680, 560, 1120, 1680, 3360, 6720, 2520
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| This is a function of the individual partitions of an integer. The number of values in each line is given by A000041; thus lines 0 to 5 of the sequence are (1), (1), (1,2), (1,3,6), (2,4,6,12,24). The partitions in each line are ordered with the largest part sizes first, so the line 4 indices are [4], [3,1], [2,2], [2,1,1] and [1,1,1,1]. Note that exponents are often used to represent repeated values in a partition, so the last index could instead be written [1^4]. The combination function (sequence A007318) C(n,m) = C([m,n-m]).
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LINKS
| T. D. Noe, Rows n=0..25 of triangle, flattened
Index entries for triangles and arrays related to Pascal's triangle.
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FORMULA
| C([<a_i>]) = (\Sigma a_i)! / \Pi a_i !
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EXAMPLE
| C([2,1]) = 3 for the labelings ({1,2},{3}), ({1,3},{2}) and ({2,3},{2}).
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MATHEMATICA
| Flatten[Table[Apply[Multinomial, Partitions[i], {1}], {i, 0, 25}] (from T. D. Noe, Oct 14 2007)
Needs["Combinatorica`"]; Flatten[ Multinomial @@@ Partitions @ # & /@ Range[ 0, 8]] (* Michael Somos Feb 05 2011 *)
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CROSSREFS
| Different from A036038.
Sequence in context: A051537 A171999 A036038 * A103280 A046899 A035206
Adjacent sequences: A078757 A078758 A078759 * A078761 A078762 A078763
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KEYWORD
| nice,easy,nonn,tabl
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 08 2003
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