A052822 A simple grammar: pairs of cycles of cycles.

0, 0, 2, 12, 80, 630, 5816, 61978, 751222, 10225140, 154610048, 2573280820, 46775427860, 922374085984, 19616567407368, 447666534959528, 10913339500879576, 283081184691349600, 7785415448640271232, 226306589802176060640, 6933002797216545295968

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..418
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 787

Programs

Maple

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

Mathematica

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

PARI

x='x+O('x^30); concat([0,0], Vec(serlaplace((log(1+log(1-x)))^2))) \\ G. C. Greubel, Aug 30 2018

Formula

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

E.g.f.: (log(1+log(1-x)))^2. - Vaclav Kotesovec, Oct 01 2013

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

Extensions

More terms from Alois P. Heinz, Mar 16 2016