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%I #13 Jun 21 2018 02:15:59
%S 1,1,2,2,3,4,5,7,9,13,16,25,31,48,64,98,133,208,291,454,657,1021,1510,
%T 2358,3545,5535,8442,13200,20319,31835,49353,77435,120711,189673,
%U 296854,467159,733363,1155646,1818594,2869377,4524081
%N Number of ways to partition n elements into pie slices each with an odd number of elements allowing the pie to be turned over.
%H Andrew Howroyd, <a href="/A032277/b032277.txt">Table of n, a(n) for n = 1..500</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%F "DIK" (bracelet, indistinct, unlabeled) transform of 1, 0, 1, 0, ... (odds)
%F G.f.: (x*(1 + x - x^4)/((1 - x)*(1 + x)*(1 - x^2 - x^4)) + Sum_{d>0} phi(d)*log((1 - x^(2*d))/(1 - x^d - x^(2*d)))/d)/2. - _Andrew Howroyd_, Jun 20 2018
%o (PARI) seq(n)={Vec(x*(1 + x - x^4)/((1 - x)*(1 + x)*(1 - x^2 - x^4)) + sum(d=1, n, eulerphi(d)/d*log((1-x^(2*d))/(1-x^d-x^(2*d)) + O(x*x^n))))/2} \\ _Andrew Howroyd_, Jun 20 2018
%K nonn
%O 1,3
%A _Christian G. Bower_
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