A052883 Expansion of e.g.f.: log((-1+x)/(-1+2*x))^2.

0, 0, 2, 18, 166, 1740, 20948, 287784, 4466712, 77539680, 1491571872, 31532466240, 727281881280, 18184495230720, 490130371249920, 14170353892047360, 437524311352665600, 14370793956158976000

Offset

0,3

Comments

Previous name was: A simple grammar.

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 856

Formula

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

Recurrence: {a(1)=0, a(0)=0, a(2)=2, (8*n+20*n^2+16*n^3+4*n^4)*a(n)+(-36-78*n-12*n^3-54*n^2)*a(n+1)+(52+13*n^2+52*n)*a(n+2)+(-6*n-15)*a(n+3)+a(n+4), a(3)=18}

a(n) ~ (n-1)! * 2^(n+1)* (log(n) + gamma - log(2)), where gamma is Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Sep 29 2013

Maple

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

Mathematica

CoefficientList[Series[Log[(-1+x)/(-1+2*x)]^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 29 2013 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(log((-1+x)/(-1+ 2*x))^2))) \\ G. C. Greubel, Sep 05 2018

Crossrefs

Sequence in context: A037728 A037623 A052865 * A052665 A259880 A364524

Adjacent sequences: A052880 A052881 A052882 * A052884 A052885 A052886

Keyword

easy,nonn

Author

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

Extensions

New name using e.g.f., Joerg Arndt, Sep 30 2013

Status

approved