OFFSET
3,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 3..200
FORMULA
a(n)=n!*sum_{j=k.. [n/2]} (-1)^j/((j-k)!*2^j*k!). E.g.f. = exp(-z^2/2)*z^(2*k) / ((1-z)*2^k*k!), where k is the number of cycles of length 2.
a(n) ~ n! * exp(-1/2)/8. - Vaclav Kotesovec, Mar 20 2014
EXAMPLE
a(4)=3 counts the 3 permutations (2143), (3412), (4321) with 2 cycles
of length 2
MAPLE
MATHEMATICA
d=Exp[-x^2/2]/(1-x); Range[0, 20]! CoefficientList[Series[(3x^4/4! )d, {x, 0, 20}], x] (* Geoffrey Critzer, Nov 29 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Weisenhorn, Jun 02 2010
EXTENSIONS
Typo in a(18) corrected by Vincenzo Librandi, Mar 21 2014
STATUS
approved