login
A simple grammar: pairs of cycles of cycles.
3

%I #22 Aug 31 2018 00:23:41

%S 0,0,2,12,80,630,5816,61978,751222,10225140,154610048,2573280820,

%T 46775427860,922374085984,19616567407368,447666534959528,

%U 10913339500879576,283081184691349600,7785415448640271232,226306589802176060640,6933002797216545295968

%N A simple grammar: pairs of cycles of cycles.

%H G. C. Greubel, <a href="/A052822/b052822.txt">Table of n, a(n) for n = 0..418</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=787">Encyclopedia of Combinatorial Structures 787</a>

%F E.g.f.: log(-1/(-1+log(-1/(-1+x))))^2.

%F E.g.f.: (log(1+log(1-x)))^2. - _Vaclav Kotesovec_, Oct 01 2013

%F a(n) ~ (n-1)! * 2*(exp(1)/(exp(1)-1))^n * (log(n) + gamma - log(exp(1)-1)), where gamma is Euler-Mascheroni constant (A001620). - _Vaclav Kotesovec_, Oct 01 2013

%p spec := [S,{B=Cycle(Z),C=Cycle(B),S=Prod(C,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%t CoefficientList[Series[(Log[1+Log[1-x]])^2, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 01 2013 *)

%o (PARI) x='x+O('x^30); concat([0,0], Vec(serlaplace((log(1+log(1-x)))^2))) \\ _G. C. Greubel_, Aug 30 2018

%K easy,nonn

%O 0,3

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

%E More terms from _Alois P. Heinz_, Mar 16 2016