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A115455
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a(n) = number of reverse alternating fixed-point-free involutions w on 1,2,...,2n, i.e. w(1)<w(2)>w(3)<w(4)>...<w(2n), w^2=1 and w(i) not= i for all i.
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1
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1, 0, 1, 1, 4, 13, 59, 308, 1871, 12879, 99144, 843735, 7865177, 79698760, 872235089, 10253148625, 128839087676, 1723418002261, 24450430660739, 366702601116524, 5796979684239647, 96339860422218143, 1679159568980521104
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| R. P. Stanley, Alternating permutations and symmetric functions, in preparation.
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LINKS
| R. P. Stanley, Permutations
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FORMULA
| sum_{n=0..infinity} a(n)x^n = (1-x^2)^{-1/4} (1+x)^{-1/2} sum_{k=0..infinity) E_{2k} v^k/k!, where E_{2k} is an Euler number and v = (1/4)log((1+x)/(1-x))
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EXAMPLE
| a(3)=1 because there is one reverse alternating fixed-point-free involution on 1,...,6, viz., 351624.
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CROSSREFS
| Cf. A007779.
Sequence in context: A158267 A026663 A149486 * A149487 A057712 A135312
Adjacent sequences: A115452 A115453 A115454 * A115456 A115457 A115458
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KEYWORD
| easy,nonn
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AUTHOR
| R. P. Stanley (rstan(AT)math.mit.edu), Jan 22 2006
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