%I #32 Jun 23 2015 03:15:26
%S 0,1,1,4,11,56,267,1730,11643,93532,804563,7789838,81109107,923080328,
%T 11250876171,147433014058,2056359699659,30514968348500,
%U 479058943716579,7942752339181286,138576460230586755,2539126631897727808,48733588613803358939
%N Number of ways to partition n labeled elements into pie slices each of at least 2 elements.
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H S. Giraudo, <a href="http://arxiv.org/abs/1306.6938">Combinatorial operads from monoids</a>, arXiv preprint arXiv:1306.6938, 2013
%H Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties </a>, arXiv:1103.2582 [math.CO], 2011-2013.
%H <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F "CIJ" (necklace, indistinct, labeled) transform of 0, 1, 1, 1...
%F E.g.f.: A(x) = log(1/(2+x-exp(x))).
%F a(n) = n! * sum(k=1..n, sum(j=0..k, binomial(k,j) *stirling2(n-k+j,j) *j!/(n-k+j)! *(-1)^(k-j))/k). - _Vladimir Kruchinin_, Feb 01 2011
%F a(n) ~ (n-1)! / (-LambertW(-1,-exp(-2))-2)^n. - _Vaclav Kotesovec_, Sep 30 2013
%t Rest[CoefficientList[Series[Log[1/(2+x-E^x)], {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, Sep 30 2013 *)
%K nonn
%O 1,4
%A _Christian G. Bower_