A052769 E.g.f.: x^3*(exp(x)-1)^2.

0, 0, 0, 0, 0, 120, 720, 2940, 10080, 31248, 90720, 251460, 673200, 1753752, 4468464, 11176620, 27518400, 66838560, 160422336, 381014676, 896518800, 2091893160, 4844402640, 11142147324, 25467789600, 57881367600, 130862253600, 294440105700, 659545876080

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 726

Programs

Maple

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

Mathematica

CoefficientList[Series[x^3*(E^x-1)^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)

PARI

seq(n)={Vec(serlaplace(x^3*(exp(x + O(x^(n-3)))-1)^2), -(n+1))} \\ Andrew Howroyd, Jan 02 2020

Formula

E.g.f.: x^3*exp(x)^2 - 2*x^3*exp(x) + x^3.

Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, (2*n^2+6*n+4)*a(n)+(-3*n^2+12)*a(n+1)+(-3*n+n^2+2)*a(n+2), a(5)= 120}.

For n<>3, a(n) = (2^n-16)*(n-2)*(n-1)*n/8. - Vaclav Kotesovec, Sep 30 2013

Extensions

New name, using e.g.f., by Vaclav Kotesovec, Sep 30 2013

Terms a(21) and beyond from Andrew Howroyd, Jan 02 2020