|
Search: id:A001758
|
|
|
| A001758 |
|
Number of quasi-alternating permutations of length n.
(Formerly M2027 N0800)
|
|
+0
5
|
|
| 1, 2, 12, 58, 300, 1682, 10332, 69298, 505500, 3990362, 33925452, 309248938, 3010070700, 31167995042, 342164637372, 3970297978978, 48558251523900, 624386836023722, 8421511353298092, 118891756573779418
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Permutations of [n] with n-2 sequences
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 113.
|
|
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!
|
|
MAPLE
|
seq(i!*coeff(series((tan(t)+sec(t))^2-4*(tan(t)+sec(t)), t, 35), t, i), i=1..24);
|
|
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 this_sequence A037133 A009618 A143770
Adjacent sequences: A001755 A001756 A001757 this_sequence A001759 A001760 A001761
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
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
|
|
|
Search completed in 0.002 seconds
|
