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A059171
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Size of largest conjugacy class in S_n, the symmetric group on n symbols.
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6
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1, 1, 3, 8, 30, 144, 840, 5760, 45360, 403200, 3991680, 43545600, 518918400, 6706022400, 93405312000, 1394852659200, 22230464256000, 376610217984000, 6758061133824000, 128047474114560000, 2554547108585472000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
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FORMULA
| a(1) = a(2) = 1; a(n) = n*(n-2)! = (n!)/(n-1) for n>2. This is the number of (n-1)-cycles in S_n.
G.f.: -ln(1-x)-x+1/(1-x). The sequence 1, 3, 8, ... has g.f. (1+x-x^2)/(1-x)^2 and a(n) = n!(n+2-0^n) = n!A065475(n). - Paul Barry, May 14 2004
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EXAMPLE
| a(3) = 3 because the largest conjugacy class in S_3 consists of the three 2-cycles {(12),(13),(23)}.
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MAPLE
| a := proc(n) if n<=2 then RETURN(1) else RETURN(n*(n-2)!) fi: end:for n from 1 to 40 do printf(`%d, `, a(n)) od:
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MATHEMATICA
| Join[{1, 1}, Table[n (n-2)!, {n, 3, 30}]] (* From Harvey P. Dale, Oct 25 2011 *)
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PROG
| (MAGMA) [1, 1], [n*Factorial(n-2): n in [3..25]]; // Vincenzo Librandi, Oct 26 2011
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CROSSREFS
| Apart from initial terms, same as A001048.
Sequence in context: A074501 A009123 A066764 * A078619 A066304 A145776
Adjacent sequences: A059168 A059169 A059170 * A059172 A059173 A059174
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Des MacHale (d.machale(AT)ucc.ie), Feb 14 2001
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Fabian Rothelius (fabian.rothelius(AT)telia.com) and James A. Sellers, Feb 15 2001
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