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

0,6

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

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

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 *)

Prog

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

Crossrefs

Sequence in context: A300299 A052787 A292970 * A179724 A052766 A052627

Adjacent sequences: A052766 A052767 A052768 * A052770 A052771 A052772

Keyword

easy,nonn

Author

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

Extensions

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

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

Status

approved