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

0, 0, 2, 15, 116, 1030, 10644, 127428, 1750944, 27325296, 479288160, 9355658400, 201405744000, 4743245520000, 121334466758400, 3350276227872000, 99309556729958400, 3145135939426252800

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 829

Crossrefs

Cf. A000629.

Programs

Maple

spec := [S,{B=Sequence(Z,1 <= card),C=Cycle(B),S=Prod(B,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

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

Formula

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

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)}.

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

Extensions

New name using e.g.f., Vaclav Kotesovec, Oct 01 2013