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Search: id:A000138
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| A000138 |
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Expansion of exp (-x^4 /4) / (1-x).
(Formerly M1635 N0638)
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+0
4
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| 1, 1, 2, 6, 18, 90, 540, 3780, 31500, 283500, 2835000, 31185000, 372972600, 4848643800, 67881013200, 1018215198000, 16294848570000, 277012425690000, 4986223662420000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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For n >= 1 a(n) is the number of permutations in the symmetric group S_n such that their cycle decomposition contains no 4-cycle.
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 85.
R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986, page 93, problem 7.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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a(n) = n! * sum i=0 ... [n/4]( (-1)^i /(i! * 4^i)); a(n)/n! ~ sum i >= 0 (-1)^i /(i! * 4^i) = e^(-1/4); a(n) ~ e^(-1/4) * n!; a(n) ~ e^(-1/4) * (n/e)^n * sqrt(2 * Pi * n). - Avi Peretz (njk(AT)netvision.net.il), Apr 22 2001
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EXAMPLE
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a(4) = 18 because in S_4 the permutations with no 4-cycle are the complement of the six 4-cycles so a(4) = 4! - 6 = 18.
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CROSSREFS
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Cf. A000142, A000090.
Sequence in context: A118476 A118455 A053505 this_sequence A028857 A052687 A056743
Adjacent sequences: A000135 A000136 A000137 this_sequence A000139 A000140 A000141
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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