%I #12 Sep 13 2018 15:44:33
%S 1,1,0,1,1,1,1,1,2,3,2,3,3,5,3,7,10,9,10,11,17,15,23,17,36,45,42,49,
%T 61,77,73,105,98,159,116,211,267,289,291,367,454,493,604,619,893,795,
%U 1175,969,1716,1937,2124,2185,2917,3225,3697,4289,4862,6147
%N Number of ways to partition n elements into pie slices of different odd sizes.
%H Andrew Howroyd, <a href="/A032154/b032154.txt">Table of n, a(n) for n = 0..1000</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>
%F "CGK" (necklace, element, unlabeled) transform of 1, 0, 1, 0, ... (odds).
%F G.f.: 1 + Sum_{k>=1} (k-1)! * x^(k^2) / (Product_{j=1..k} 1-x^(2*j)). - _Andrew Howroyd_, Sep 13 2018
%o (PARI) seq(n)=[subst(serlaplace(p/y),y,1) | p <- Vec(y-1+prod(k=1, ceil(n/2), 1 + x^(2*k-1)*y + O(x*x^n)))] \\ _Andrew Howroyd_, Sep 13 2018
%o (PARI) seq(n)={Vec(1 + sum(k=1, sqrtint(n), my(r=k^2); (k-1)! * x^r / prod(j=1, k, 1 - x^(2*j) + O(x*x^(n-r)))))} \\ _Andrew Howroyd_, Sep 13 2018
%K nonn
%O 0,9
%A _Christian G. Bower_
%E a(0)=1 prepended by _Andrew Howroyd_, Sep 13 2018