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Search: id:A001758
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| A001758 |
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Number of quasi-alternating permutations of length n.
(Formerly M2027 N0800)
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+0
5
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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; listen)
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OFFSET
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1,2
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COMMENT
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Permutations of [n] with n-2 sequences
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 113.
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FORMULA
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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
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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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CROSSREFS
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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.
Adjacent sequences: A001755 A001756 A001757 this_sequence A001759 A001760 A001761
Sequence in context: A094780 A100103 A054145 this_sequence A037133 A009618 A143770
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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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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