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A052861 E.g.f.: log((1-x)/(1-2*x))*x/(1-x).

%I A052861 #18 Apr 18 2017 07:04:11
%S A052861 0,0,2,15,116,1030,10644,127428,1750944,27325296,479288160,9355658400,
%T A052861 201405744000,4743245520000,121334466758400,3350276227872000,
%U A052861 99309556729958400,3145135939426252800
%N A052861 E.g.f.: log((1-x)/(1-2*x))*x/(1-x).
%C A052861 Previous name was: A simple grammar.
%H A052861 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=829">Encyclopedia of Combinatorial Structures 829</a>
%F A052861 E.g.f.: -log((-1+x)/(-1+2*x))*x/(-1+x).
%F A052861 Recurrence: {a(1)=0, a(0)=0, a(2)=2, (-2*n^4-12*n^3-22*n^2-12*n)*a(n)+(5*n^3+28*n^2+45*n+18)*a(n+1)+(-17*n-15-4*n^2)*a(n+2)+(n+2)*a(n+3)}.
%F A052861 a(n) ~ (n-1)! * 2^n * (1 + 2/n + 6/n^2 + 26/n^3 + 150/n^4 + 1082/n^5 + 9366/n^6 + 94586/n^7), coefficients are A000629. - _Vaclav Kotesovec_, Mar 17 2015
%p A052861 spec := [S,{B=Sequence(Z,1 <= card),C=Cycle(B),S=Prod(B,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052861 CoefficientList[Series[Log[(1-x)/(1-2*x)]*x/(1-x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 01 2013 *)
%t A052861 Flatten[{0,Table[FullSimplify[-n!*(EulerGamma + I*Pi + 2^n*LerchPhi[2,1,n] + PolyGamma[0,n])],{n,1,20}]}] (* _Vaclav Kotesovec_, Oct 01 2013 *)
%Y A052861 Cf. A000629.
%K A052861 easy,nonn
%O A052861 0,3
%A A052861 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052861 New name using e.g.f., _Vaclav Kotesovec_, Oct 01 2013