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%I #23 Sep 06 2018 03:02:01
%S 0,0,2,12,72,500,4080,38668,419160,5124708,69831360,1049972924,
%T 17273719848,308714206996,5956836347280,123437573728620,
%U 2734197673727736,64473939310567364,1612626113517932640,42645398700110627356,1188880256538133537224,34849264499702702749812
%N Expansion of e.g.f.: (log(2-exp(x)))^2.
%C Previous name was: A simple grammar.
%H G. C. Greubel, <a href="/A052833/b052833.txt">Table of n, a(n) for n = 0..424</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=799">Encyclopedia of Combinatorial Structures 799</a>
%F E.g.f.: log(-1/(-2+exp(x)))^2.
%F a(n) ~ (n-1)! * 2*(log(n) + gamma - log(2) - log(log(2)))/log(2)^n, where gamma is Euler-Mascheroni constant (A001620). - _Vaclav Kotesovec_, Sep 30 2013
%p spec := [S,{B=Set(Z,1 <= card),C=Cycle(B),S=Prod(C,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t CoefficientList[Series[Log[2-E^x]^2, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 30 2013 *)
%o (PARI) x='x+O('x^30); concat([0,0], Vec(serlaplace((log(2-exp(x)))^2))) \\ _G. C. Greubel_, Sep 05 2018
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E New name, using e.g.f., by _Vaclav Kotesovec_, Sep 30 2013
%E More terms from _Alois P. Heinz_, Mar 16 2016
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