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 A002484 Number of ménage permutations. (Formerly M1524 N0597) 1
 1, 2, 5, 20, 87, 616, 4843, 44128, 444621, 4936274, 59661265, 780547332, 10987097799, 165587196328, 2660378564791, 45392026278108, 819716784789209, 15620011000052754, 313219935456572497, 6593238656843759572 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 REFERENCES C. Berge, Principles of Combinatorics, Academic Press, NY, 1971, p. 162. E. N. Gilbert, Knots and classes of menage permutations, Scripta Math., 22 (1956), 228-233 (1957). J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 195. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 3..200 E. N. Gilbert, Knots and classes of menage permutations [Annotated scanned copy of preprint] FORMULA Gilbert gives a formula (see Maple code). a(n) ~ (n-1)! * exp(-2). - Vaclav Kotesovec, May 23 2014 MAPLE with(numtheory): d := n->divisors(n): U := (m, t)->sum(2*m*binomial(2*m-k, k)*(m-k)!*(t-1)^k/(2*m-k), k=0..m): A := (n, i)->phi(n/dd[i])*(n/dd[i])^dd[i]*U(dd[i], 1-dd[i]/n)/n: for n from 3 to 28 do dd := d(n): B := [seq(A(n, j), j=1..nops(dd))]: a[n] := sum(B[i], i=1..nops(B)) od: seq(a[n], n=3..28); # Emeric Deutsch, Mar 08 2004 MATHEMATICA u[m_, t_] := Sum[ 2m*Binomial[ 2m-k, k]*(m-k)!*((t-1)^k / (2m-k)), {k, 0, m}]; a[n_] := Sum[ EulerPhi[n/d] * (n/d)^d * (u[d, 1-d/n]/n), {d, Divisors[n]} ]; Table[ a[n], {n, 3, 22} ] (* Jean-François Alcover, Dec 07 2011, after Maple *) CROSSREFS Cf. A000179. Sequence in context: A262171 A262172 A258830 * A277686 A115082 A020105 Adjacent sequences:  A002481 A002482 A002483 * A002485 A002486 A002487 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS More terms from Emeric Deutsch, Mar 08 2004 STATUS approved

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