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 A024168 n!(1/2 - 1/3 + .. + c/n), where c = (-1)^n. 2
 0, 1, 1, 10, 26, 276, 1212, 14736, 92304, 1285920, 10516320, 166112640, 1680462720, 29753498880, 359124192000, 7053661440000, 98989454592000, 2137497610752000, 34210080898560000, 805846718380032000, 14489879077804032000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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 LINKS Wikipedia, One hundred prisoners. FORMULA E.g.f.: (x-log(1+x))/(1-x). a(n)=a(n-1)+a(n-2)*(n-1)^2, n>2. MATHEMATICA 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 *) CROSSREFS 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 KEYWORD nonn AUTHOR EXTENSIONS Formulae and more terms from Michael Somos, Oct 29, 2002 STATUS approved

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