A052784 E.g.f.: x^3*(exp(x)-1)^3.

0, 0, 0, 0, 0, 0, 720, 7560, 50400, 272160, 1300320, 5738040, 23958000, 96061680, 373477104, 1417295880, 5274360000, 19313985600, 69770966976, 249130574424, 880629138000

Offset

0,7

Comments

Previous name was: A simple grammar.

Links

Table of n, a(n) for n=0..20.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 741

Formula

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

D-finite Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (-36*n^2-66*n-6*n^3-36)*a(n)+(-44*n+11*n^3+33*n^2-132)*a(n+1)+(-6*n^3-36+42*n)*a(n+2)+(-3*n^2+n^3+2*n)*a(n+3)=0}

For n>3 , a(n) = (n-2)*(n-1)*n*(3^(n-3) - 3*2^(n-3) + 3). - Vaclav Kotesovec, Oct 01 2013

Maple

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

Mathematica

CoefficientList[Series[x^3*(E^x-1)^3, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)

Crossrefs

Sequence in context: A153760 A029574 A119540 * A052786 A187192 A052792

Adjacent sequences: A052781 A052782 A052783 * A052785 A052786 A052787

Keyword

easy,nonn

Author

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

Extensions

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

Status

approved