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A002484
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Number of menage permutations.
(Formerly M1524 N0597)
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0
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1, 2, 5, 20, 87, 616, 4843, 44128, 444621, 4936274, 59661265, 780547332, 10987097799, 165587196328, 2660378564791, 45392026278108, 819716784789209, 15620011000052754, 313219935456572497, 6593238656843759572
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OFFSET
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3,2
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=3..22.
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FORMULA
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Gilbert gives a formula (see Maple code).
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MAPLE
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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);
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MATHEMATICA
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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} ] (* From Jean-François Alcover, Dec 07 2011, after Maple *)
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CROSSREFS
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Sequence in context: A170947 A006228 A190656 * A003069 A115082 A020105
Adjacent sequences: A002481 A002482 A002483 * A002485 A002486 A002487
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms and Maple code from Emeric Deutsch, Mar 08 2004
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STATUS
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approved
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