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A216778
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Number of derangements on n elements with an even number of cycles.
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4
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1, 0, 0, 0, 3, 20, 130, 924, 7413, 66744, 667476, 7342280, 88107415, 1145396460, 16035550518, 240533257860, 3848532125865, 65425046139824, 1177650830516968, 22375365779822544, 447507315596451051, 9397653627525472260, 206748379805560389930, 4755212735527888968620
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n+1) = n*(a(n) + a(n-1) + n - 2), a(0)=1, a(1)=0.
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MAPLE
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a := proc (n) local x, y, t, k; if n = 0 then 1 elif n = 1 then 0 else x := 1; y := 0; for k from 2 to n do t := y; y := (k-1)*(x+y+k-3); x := t end do; y end if end proc;
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MATHEMATICA
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nn=23; Range[0, nn]!*CoefficientList[Series[Cosh[Log[1/(1-x)]-x], {x, 0, nn}], x] (* Geoffrey Critzer, Jun 23 2014 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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