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A049009
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Number of functions from a set to itself such that the sizes of the pre-images of the individual elements in the range form the n-th partition in Abramowitz and Stegun order.
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7
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1, 2, 2, 3, 18, 6, 4, 48, 36, 144, 24, 5, 100, 200, 600, 900, 1200, 120, 6, 180, 450, 300, 1800, 7200, 1800, 7200, 16200, 10800, 720, 7, 294, 882, 1470, 4410, 22050, 14700, 22050, 29400, 176400, 88200, 88200, 264600, 105840, 5040, 8, 448, 1568, 3136, 1960
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n,k) is a refinement of 1; 2,2; 3,18,6; 4,84,144,24; ... cf. A019575.
a(n,k)/A036040(n,k) and a(n,k)/A048996(n,k) are also integer sequences.
Apparently a(n,k)/A036040(n,k) = A178888(n,k) - R. J. Mathar, Apr 17 2011
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
| a(n,k) = A036038(n,k) * A035206(n,k).
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EXAMPLE
| Table begins
1;
2,2;
3,18,6;
4,48,36,144,24;
...
For n = 4, partition [3], we can map all three of {1,2,3} to any one of them, for 3 possible values. For n=5, partition [2,1], there are 3 choices for which element is alone in a preimage, 3 choices for which element to map that to and then 2 choices for which element to map the pair to, so a(5) = 3*3*2 = 18.
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CROSSREFS
| A036038, A035206, A019575, A036040, A048996.
Row sizes A000041, sums A000312.
Sequence in context: A089751 A137909 A035796 * A101817 A058159 A058157
Adjacent sequences: A049006 A049007 A049008 * A049010 A049011 A049012
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KEYWORD
| nonn,tabf,easy
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com)
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EXTENSIONS
| Better definition from Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 30 2006
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