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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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3
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1, 6, 1456, 2020656, 9336345856, 108480272749056, 2664103110372192256, 122840808510269863827456, 9758611490955498257378246656, 1251231616578606273788469919481856
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Bisection of A005981.
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LINKS
| 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
| 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
| 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
| Cf. A000111, A005981, A058257, A131454, A131455.
Sequence in context: A195646 A199645 A107252 * A160226 A034841 A149187
Adjacent sequences: A131450 A131451 A131452 * A131454 A131455 A131456
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KEYWORD
| easy,nonn
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AUTHOR
| Peter Bala (pbala(AT)toucansurf.com), Jul 13 2007
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