

A060706


For n >= 1 a(n) is the size of the conjugacy class in the symmetric group S_(4n) consisting of permutations whose cycle decomposition is a product of n disjoint 4cycles.


6



1, 6, 1260, 1247400, 3405402000, 19799007228000, 210384250804728000, 3692243601622976400000, 99579809935771673508000000, 3910499136177753618659160000000, 214428309633170941925556379440000000
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OFFSET

0,2


COMMENTS

a(n) is the number of ways to seat 4n bridge players at n circular tables with four players at each table.  Geoffrey Critzer, Dec 17 2011


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..100


FORMULA

a(n) = (4n)! / (n! * 4^n). Recursion: a(0) = 1, a(1) = 6, for n >= 2 a(n) = a(n1) * C(4n  1, 3)* 6 = a(n1)*(4n1)*(4n2)*(4n3). Using Stirling's formula in A000142 we have a(n) ~ 2 * 64^n * (n/e)^(3n).
E.g.f.: exp(x^4/4).  Geoffrey Critzer, Dec 17 2011
Write the generating function for this sequence in the form A(x) = sum_{n>=0} a(n)* x^(3*n+1)/(3*n+1)!. Then A'(x)*( 1  A(x)^3) = 1, consequently A(x) is a root of z^4  4*z + 4*x with A(0) = 0. Cf. A052502.  Peter Bala, Jan 02 2015


MAPLE

for n from 0 to 20 do printf(`%d, `, (4*n)! / (n! * 4^n)) od:


MATHEMATICA

nn = 40; a = x^4/4; f[list_] := Select[list, # > 0 &];
f[Range[0, nn]! CoefficientList[Series[Exp[a], {x, 0, nn}], x]] (* Geoffrey Critzer, Dec 17 2011 *)


PROG

(PARI) { for (n=0, 100, write("b060706.txt", n, " ", (4*n)! / (n! * 4^n)); ) } \\ Harry J. Smith, Jul 09 2009


CROSSREFS

Cf. A000142. A001147, A052502, A052504.
Sequence in context: A263437 A001324 A183585 * A052278 A264103 A202381
Adjacent sequences: A060703 A060704 A060705 * A060707 A060708 A060709


KEYWORD

nonn


AUTHOR

Ahmed Fares (ahmedfares(AT)mydeja.com), Apr 21 2001


EXTENSIONS

More terms from James A. Sellers, Apr 23 2001


STATUS

approved



