2,3

Also: odd permutations of length n with no fixed points. - Martin Wohlgemuth (mail(AT)matroid.com), May 31 2003

Also number of cycles of length 2 in all derangements of [n]. Example: a(4)=6 because in the derangements of [4], namely (1432), (1342), (13)(24), (1423), (12)(34), (1243), (1234), (1324), and (14)(23), we have altogether 6 cycles of length 2. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 31 2009]

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).

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 65.

M. Wohlgemuth Derangements revisited

a(n) = sum((-1)^j*n!/(2!*j!), j=2..n-2)

a(n) = A000166(n-2)*binomial(n, 2). - David Wasserman (wasserma(AT)spawar.navy.mil), Aug 13 2004

Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 22 2009: (Start)

E.g.f.: G=z^2*exp(-z)/[2(1-z)].

(End)

a(4)=6 because we have 1243, 1432, 1324, 4231, 3214, and 2134. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 31 2009]

a:=n->sum(n!*sum((-1)^k/(k-1)!, j=0..n), k=1..n): seq(-a(n)/2!, n=1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 18 2007

Table[Subfactorial[n - 2]*Binomial[n, 2], {n, 2, 22}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]

Cf. A000240, A000449, A000475.

A diagonal of A008291.

a(n)+A0003221(n)=A000166(n).

Adjacent sequences: A000384 A000385 A000386 this_sequence A000388 A000389 A000390

Sequence in context: A114959 A000386 A145221 this_sequence A027148 A095854 A027268

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).