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A024168
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n!(1/2 - 1/3 + .. + c/n), where c = (-1)^n.
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2
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0, 1, 1, 10, 26, 276, 1212, 14736, 92304, 1285920, 10516320, 166112640, 1680462720, 29753498880, 359124192000, 7053661440000, 98989454592000, 2137497610752000, 34210080898560000, 805846718380032000, 14489879077804032000
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OFFSET
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1,4
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COMMENTS
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a(n) is the number of permutations of n letters all cycles of which have length <= n/2, a quantity which arises in the solution to the One Hundred Prisoners problem. - Jim Ferry (jferry(AT)alum.mit.edu), Mar 29 2007
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LINKS
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Table of n, a(n) for n=1..21.
Index entries for sequences related to factorial numbers
Wikipedia, One hundred prisoners.
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FORMULA
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E.g.f.: (x-log(1+x))/(1-x). a(n)=a(n-1)+a(n-2)*(n-1)^2, n>2.
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MATHEMATICA
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f[k_] := (k + 1) (-1)^(k + 1)
t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}] (* A024168 signed *)
(* Clark Kimberling, Dec 30 2011 *)
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CROSSREFS
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A075829(n)=a(n-1)/gcd(a(n-1), a(n))
Sequence in context: A221568 A092774 A217583 * A043107 A039284 A045177
Adjacent sequences: A024165 A024166 A024167 * A024169 A024170 A024171
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling
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EXTENSIONS
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Formulae and more terms from Michael Somos, Oct 29, 2002
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STATUS
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approved
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