cp's OEIS Frontend

A208186 Number of distinct n-colored necklaces with 5 beads per color.

%I A208186 #10 Dec 01 2014 20:21:25
%S A208186 1,1,26,50452,586637256,24934429725024,2961088201992945120,
%T A208186 823940558733748910598720,474389544274867071519255599040,
%U A208186 515190840198859838606483730223480320,982409170121762644481286121423409538362880,3106878824601775580798512171862746898249905228800
%N A208186 Number of distinct n-colored necklaces with 5 beads per color.
%H A208186 Alois P. Heinz, <a href="/A208186/b208186.txt">Table of n, a(n) for n = 0..50</a>
%F A208186 a(n) = Sum_{d|5} phi(5/d)*(n*d)!/(d!^n*n*5) if n>0 and a(0) = 1.
%e A208186 a(0) =  1: the empty necklace.
%e A208186 a(1) =  1: {00000}.
%e A208186 a(2) = 26: {0000011111, ..., 0101010101}.
%p A208186 with(numtheory);
%p A208186 a:= n-> `if`(n=0, 1, add(phi(5/d) *(n*d)!/(d!^n *5*n), d={1, 5})):
%p A208186 seq(a(n), n=0..12);
%Y A208186 Row n=5 of A208183.
%Y A208186 Cf. A000010, A000142.
%K A208186 nonn
%O A208186 0,3
%A A208186 _Alois P. Heinz_, Feb 24 2012