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%I #15 Sep 08 2022 08:44:39
%S 1,6,720,72,239500800,1307674368000,6402373705728000,
%T 51090942171709440000,310224200866619719680000,648,
%U 265252859812191058636308480000000
%N Order of shuffle group for deck of 3n cards.
%D W. Bosma et al., Solving Problems with Magma, Sect. 2.2.3.
%D Cannon and Playoust, An Introduction to MAGMA, Section 6.3.1.
%H Sean A. Irvine, <a href="/A014525/b014525.txt">Table of n, a(n) for n = 0..33</a>
%F Conjecture: a(3^m) = (m+1) * 6^(m+1), a(4*m) = (1/2) * (3*4*m)!, otherwise a(n) = (3*n)!. - _Sean A. Irvine_, Nov 07 2018
%o (Magma) SG := function(n) m := 3*n; G := SymmetricGroup(m); p := &*[ G | (i,i+2*n): i in [ 1..n ]]; q := &*[ G | (i,i+n,i+2*n): i in [ 1..n ]]; s := [ ((i-1) mod 3 ) * n + (i-1) div 3 + 1: i in [ 1..m ]]; return Order(sub<G | p, q, s >); end function;
%Y Cf. A014766.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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