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A161132
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Number of permutations of {1,2,...,n} that have no even fixed points.
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2
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1, 1, 1, 4, 14, 78, 426, 3216, 24024, 229080, 2170680, 25022880, 287250480, 3884393520, 52370755920, 812752093440, 12585067447680, 220448163358080, 3854801333416320, 75225258805132800, 1465957162768492800
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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a(n)=Sum[d(n-j)*binom(ceil(n/2), j), j=0..ceil(n/2)], where d(i)=A000166(i) are the derangement numbers.
a(n)=Sum[(-1)^(j)*binomial(floor(n/2),j)*(n-j)!, j=0..floor(n/2)].
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EXAMPLE
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a(3)=4 because we have 132, 312, 213, and 231.
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MAPLE
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d[0] := 1: for n to 25 do d[n] := n*d[n-1]+(-1)^n end do: a := proc (n) options operator, arrow: add(d[n-j]*binomial(ceil((1/2)*n), j), j = 0 .. ceil((1/2)*n)) end proc: seq(a(n), n = 0 .. 22);
a := proc (n) options operator, arrow: add((-1)^j*binomial(floor((1/2)*n), j)*factorial(n-j), j = 0 .. floor((1/2)*n)) end proc; seq(a(n), n = 0 .. 22); [From Emeric Deutsch, Jul 18 2009]
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CROSSREFS
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A000166, A161131
Sequence in context: A222900 A222485 A009347 * A186638 A187847 A003707
Adjacent sequences: A161129 A161130 A161131 * A161133 A161134 A161135
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, Jul 18 2009
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STATUS
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approved
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