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Search: id:A131453
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| A131453 |
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2 up, 2 down, ..., 2 up, 2 down permutations of length 4n+1. |
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+0
4
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| 1, 6, 1456, 2020656, 9336345856, 108480272749056, 2664103110372192256, 122840808510269863827456, 9758611490955498257378246656, 1251231616578606273788469919481856
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Bisection of A005981.
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LINKS
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B.Shapiro, A. Vainshtein, Counting real rational functions with all real critical values, Moscow Math. J., 3 (2003), 647-659.
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FORMULA
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E.g.f.: sum_ {n = 0 .. inf} a(n)*(x^(4n+1))/(4n+1)! = (sin(x)*(exp(2x)+1)+cos(x)*(exp(2x)-1))/(2*exp(x)+cos(x)*(exp(2x)+1)).
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EXAMPLE
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a(1)=6. The six 2 up, 2 down permutations on 5 letters are (12543), (13542), (14532), (23541), (24532) and (34521).
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CROSSREFS
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Cf. A000111, A005981, A058257, A131454, A131455.
Sequence in context: A055306 A066037 A107252 this_sequence A160226 A034841 A149187
Adjacent sequences: A131450 A131451 A131452 this_sequence A131454 A131455 A131456
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KEYWORD
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easy,nonn
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AUTHOR
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Peter Bala (pbala(AT)toucansurf.com), Jul 13 2007
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