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Search: id:A002484
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| A002484 |
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Number of menage permutations.
(Formerly M1524 N0597)
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+0
1
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| 1, 2, 5, 20, 87, 616, 4843, 44128, 444621, 4936274, 59661265, 780547332, 10987097799, 165587196328, 2660378564791, 45392026278108, 819716784789209, 15620011000052754, 313219935456572497, 6593238656843759572
(list; graph; listen)
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OFFSET
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3,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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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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CROSSREFS
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Adjacent sequences: A002481 A002482 A002483 this_sequence A002485 A002486 A002487
Sequence in context: A008983 A012768 A006228 this_sequence A003069 A115082 A020105
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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 (njas(AT)research.att.com).
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EXTENSIONS
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More terms and Maple code from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 08 2004
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