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A029571
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Number of permutations of an n-set containing a 4-cycle.
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3
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0, 0, 0, 0, 6, 30, 180, 1260, 8820, 79380, 793800, 8731800, 106029000, 1378377000, 19297278000, 289459170000, 4627941318000, 78675002406000, 1416150043308000, 26906850822852000, 538156815464268000
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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) = n! * (1 - sum(k=0..floor(n/4), (-1)^k/(k!*4^k) ) ).
a(n)/n! is asymptotic to 1-e^(-1/4) = 1 - A092616.
a(n) = n! (1 - Gamma(floor(n/4)+1,-1/4)*exp(1/4)/(floor(n/4))!). - Robert Israel, Dec 07 2016
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MAPLE
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L:= [seq( 1 - add((-1)^k/(k!*4^k), k=0..m), m=0..10)]:
seq(seq((4*m+j)!*L[m+1], j=0..3), m=0..10); # Robert Israel, Dec 07 2016
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MATHEMATICA
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a[n_] := n! (1 - Sum[(-1)^k/(k! 4^k), {k, 0, Floor[n/4]}]);
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PROG
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(PARI) a(n)=n! * (1 - sum(k=0, floor(n/4), (-1)^k/(k!*4^k) ) ); \\ Joerg Arndt, Aug 08 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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