N. J. A. Sloane njas at
Sun Jan 27 19:09:59 CET 2002

when you copy the present entry, please be sure not to
leave out any lines!

some lines are very long.  the best thing
is to break them with a "newline"



%C A062282 Let d(n) be the number of derangements of n elements (sequence A000166) then a(n) has the recursio
n: a(n) = d(n) + C(n,2)*d(n-2) + C(n,4)*d(n-4) + C(n,6)*d(n-6)... = A000166(n) + A000387(n) + A000475(n) + C(
n,6)*d(n-6)... The E.g.f for a(n) is: cosh(x) * exp(-x)/(1-x) and the asymptotic expression for a(n) is: a(n)
 ~ n! * (1 + 1/e^2)/2 i.e. as n goes to infinity the fraction of permutations that has an even number of fixe
d points is about (1 + 1/e^2)/2 = 0.567667...

I see my mouse has done the right thing:  just break it up.
Don't add slashes at the end of lines

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