A052799 Expansion of e.g.f.: x^4*(log(1-x))^2.

0, 0, 0, 0, 0, 0, 720, 5040, 36960, 302400, 2761920, 27941760, 310495680, 3760922880, 49324923648, 696388492800, 10530709862400, 169811234611200, 2908629247795200, 52738216760033280, 1009115747652096000

Offset

0,7

Comments

Previous name was: A simple grammar.

Links

G. C. Greubel, Table of n, a(n) for n = 0..449

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 757

Formula

E.g.f.: x^4*log(-1/(-1+x))^2.

Recurrence: a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (-5*n^3+n^4+32*n-6*n^2+32)*a(n)+(9*n^2+5*n-2*n^3-42)*a(n+1)+(n^2-5*n+6)*a(n+2) = 0.

a(n) ~ (n-1)! * 2*(log(n) + gamma), where gamma is Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Oct 01 2013

a(n) = n*A052766(n-1) = 2*4!*binomial(n,4)*abs(Stirling1(n-4,2)) for n >= 4. - Andrew Howroyd, Aug 08 2020

Maple

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

Mathematica

CoefficientList[Series[x^4*(Log[1-x])^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)

Prog

(PARI) x='x+O('x^30); concat(vector(6), Vec(serlaplace(x^4*(log(1-x))^2))) \\ G. C. Greubel, Sep 05 2018
(PARI) a(n)={if(n>=4, 2*4!*binomial(n, 4)*abs(stirling(n-4, 2, 1)), 0)} \\ Andrew Howroyd, Aug 08 2020

Crossrefs

Cf. A052766.

Sequence in context: A053625 A052793 A179728 * A229569 A179964 A153760

Adjacent sequences: A052796 A052797 A052798 * A052800 A052801 A052802

Keyword

easy,nonn

Author

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

Extensions

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

Status

approved