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A000704
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Number of degree-n even permutations of order dividing 2.
(Formerly M3511 N1427)
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13
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1, 1, 1, 1, 4, 16, 46, 106, 316, 1324, 5356, 18316, 63856, 272416, 1264264, 5409496, 22302736, 101343376, 507711376, 2495918224, 11798364736, 58074029056
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Number of odd partitions of an n-element set avoiding the pattern 123 (see Goyt paper). - Ralf Stephan, May 08 2007
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REFERENCES
| L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
A. M. Goyt, Avoidance of partitions of a 3-element set
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FORMULA
| E.g.f.: e^x cosh ( x^2 / 2 ).
a(n) = sum[i=0,floor(n/4), C(n,4i)*(4i-1)!! ]. - Ralf Stephan, May 08 2007 [Corrected by Sean A. Irvine 1 Mar 2011]
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MATHEMATICA
| f[n_] := Sum[(4i - 1)!! Binomial[n, 4i], {i, 0, n/4}]; Array[f, 22, 0] (* RGWv *)
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CROSSREFS
| Sequence in context: A134139 A097125 A159940 * A007315 A055342 A174836
Adjacent sequences: A000701 A000702 A000703 * A000705 A000706 A000707
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
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