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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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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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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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Sequence in context: A008983 A012768 A006228 this_sequence A003069 A115082 A020105
Adjacent sequences: A002481 A002482 A002483 this_sequence 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 (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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