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%I #12 Sep 13 2018 15:45:41
%S 1,0,1,1,1,2,2,3,3,6,6,9,11,14,22,27,35,46,62,73,119,138,190,239,323,
%T 402,522,753,927,1218,1574,2039,2599,3390,4154,6013,7247,9574,12026,
%U 15807,19615,25598,31850,40293,54795,67530,86202,109851
%N Number of ways to partition n elements into pie slices of different sizes other than one.
%H Andrew Howroyd, <a href="/A032155/b032155.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 0, 1, 1, 1, ...
%F G.f.: 1 + Sum_{k>=1} (k-1)! * x^((k^2+3*k)/2) / (Product_{j=1..k} 1-x^j). - _Andrew Howroyd_, Sep 13 2018
%o (PARI) seq(n)=[subst(serlaplace(p/y*y^0),y,1) | p <- Vec(y-1+prod(k=2, n, 1 + x^k*y + O(x*x^n)))] \\ _Andrew Howroyd_, Sep 13 2018
%o (PARI) seq(n)={Vec(1 + sum(k=1, n, my(r=(k^2+3*k)/2); if(r<=n, (k-1)! * x^r / prod(j=1, k, 1 - x^j + O(x*x^(n-r))))))} \\ _Andrew Howroyd_, Sep 13 2018
%K nonn
%O 0,6
%A _Christian G. Bower_
%E a(0)=1 prepended by _Andrew Howroyd_, Sep 13 2018
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