A032261 - OEIS

%I #16 Sep 13 2018 15:47:13

%S 1,3,9,27,243,2916,43740,787320,16533720,396809280,10713850560,

%T 321415516800,10606712054400,381841633958400,14891823724377600,

%U 625456596423859200,28145546839073664000,1350986248275535872000

%N Number of bracelets with n labeled beads of 3 colors.

%H Andrew Howroyd, <a href="/A032261/b032261.txt">Table of n, a(n) for n = 0..200</a>

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

%F "DIJ" (bracelet, indistinct, labeled) transform of 3, 0, 0, 0, ...

%F a(n) = 3^n*(n-1)!/2 for n >= 3.

%F E.g.f.: 1 + (g(x) + g(x)^2/2 - log(1-g(x)))/2 where g(x) = 3*x. - _Andrew Howroyd_, Sep 12 2018

%o (PARI) a(n)={3^n*if(n<3, 1, (n-1)!/2)} \\ _Andrew Howroyd_, Sep 12 2018

%o (PARI) seq(n)={my(p=3*x + O(x*x^n)); Vec(1 + serlaplace(p + p^2/2 - log(1-p))/2)} \\ _Andrew Howroyd_, Sep 12 2018

%K nonn,easy

%O 0,2

%A _Christian G. Bower_

%E a(0)=1 prepended by _Andrew Howroyd_, Sep 12 2018