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Search: id:A137775
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| A137775 |
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Number of triples of permutations on n letters such that for each j, exactly one of the permutations fixes j and the other two have the same image on j. |
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+0
1
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| 0, 3, 6, 45, 252, 1935, 16146, 153657, 1616760, 18699579, 235498590, 3207570597, 46968796404, 735689606535, 12272343940458, 217191191400945, 4064131571557104, 80166987477918963, 1662468879466624950
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OFFSET
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1,2
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COMMENT
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This sequence arises in a calculation of the fourth moments of the volumes of random polytopes in certain very symmetric convex bodies.
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REFERENCES
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M. Meckes, Volumens of symmetric random polytopes, Arch. Math. 82 (2004) 85--96.
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FORMULA
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a(n) = n(a(n-1)+3*a(n-2)) with a(0)=1; exponential generating function = exp(-3x)/(1-x)^3.
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EXAMPLE
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a(2)=3 because one of the permutations must be the identity and the other two are the transposition (1 2); there are three ways to pick which is the identity.
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CROSSREFS
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Cf. A000166.
Sequence in context: A009581 A088674 A076170 this_sequence A038050 A032322 A111752
Adjacent sequences: A137772 A137773 A137774 this_sequence A137776 A137777 A137778
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KEYWORD
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nonn
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AUTHOR
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Mark W. Meckes (mark.meckes(AT)case.edu), May 06 2008
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