|
|
A347106
|
|
Number of derangements of [n] having an even number of 2-cycles.
|
|
2
|
|
|
1, 0, 0, 2, 9, 24, 160, 1350, 10353, 89936, 910656, 10070730, 120546745, 1566125352, 21934589664, 329037515534, 5264316535905, 89493067364640, 1610885172539008, 30606819613112466, 612136012448309481, 12854856587833586360, 282806860558105285920
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: (exp(-x)+exp(-x*(x+1)))/(2-2*x).
a(n) = Sum_{k=0..floor(n/4)} A162974(n,2*k).
|
|
EXAMPLE
|
a(3) = 2: (123), (132).
a(4) = 9: (12)(34), (13)(24), (14)(23), (1234), (1243), (1324), (1342), (1423), (1432).
|
|
MAPLE
|
b:= proc(n, t) option remember; `if`(n=0, t, add(b(n-j,
`if`(j=2, 1-t, t))*binomial(n-1, j-1)*(j-1)!, j=2..n))
end:
a:= n-> b(n, 1):
seq(a(n), n=0..27);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|