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A001758
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Number of quasi-alternating permutations of length n.
(Formerly M2027 N0800)
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4
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1, 2, 12, 58, 300, 1682, 10332, 69298, 505500, 3990362, 33925452, 309248938, 3010070700, 31167995042, 342164637372, 3970297978978, 48558251523900, 624386836023722, 8421511353298092, 118891756573779418
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Permutations of [n] with n-2 sequences
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 113.
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).
D. Andre, Etude sur les maxima, minima et sequences des permutations, Annales scientifiques de l'E.N.S. 3e serie, tome 1 (1884), 121-134. [From Ira Gessel (gessel(AT)brandeis.edu), Apr 04 2010]
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FORMULA
| E.g.f.: u(t)^2-4u(t) where u(t)=(tan(t)+sec(t))
Asymptotics: a(n) ~ 8(2/Pi)^(n+1)((n+1)/Pi-1))n!
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MAPLE
| seq(i!*coeff(series((tan(t)+sec(t))^2-4*(tan(t)+sec(t)), t, 35), t, i), i=1..24);
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MATHEMATICA
| With[{nn=30}, Join[{1}, Drop[CoefficientList[Series[(Tan[x]+Sec[x])^2- 4(Tan[x]+Sec[x]), {x, 0, nn}], x]Range[0, nn]!, 3]]] (* From Harvey P. Dale, Oct 01 2011 *)
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CROSSREFS
| Equals 2*A000708. The diagonal P(n, n-2) of A059427.
a(n)=A001250(n+1)-2*A001250(n)
Cf. A001759, A001760, A001250.
See A008970 for formulae.
Sequence in context: A094780 A100103 A054145 * A037133 A009618 A143770
Adjacent sequences: A001755 A001756 A001757 * A001759 A001760 A001761
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Feb 01 2001
E.g.f., asymptotics and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 3/12/01
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