A052800 E.g.f.: x^5*exp(x)-x^5.

0, 0, 0, 0, 0, 0, 720, 2520, 6720, 15120, 30240, 55440, 95040, 154440, 240240, 360360, 524160, 742560, 1028160, 1395360, 1860480, 2441880, 3160080, 4037880, 5100480, 6375600, 7893600, 9687600, 11793600, 14250600, 17100720, 20389320, 24165120

Offset

0,7

Comments

Previous name was: A simple grammar.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 758

Formula

E.g.f.: x^5*exp(x)-x^5

Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (-1-n)*a(n)+(-4+n)*a(n+1)}

Maple

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

Mathematica

Flatten[{0, 0, 0, 0, 0, 0, Table[Binomial[n-1, 5]*5!, {n, 7, 35}]}] (* Vaclav Kotesovec, Oct 28 2012 *)
CoefficientList[Series[x^5 Exp[x] - x^5, {x, 0, 30}], x] Table[n!, {n, 0, 30} (* Vincenzo Librandi, May 04 2013 *)

Prog

(Magma) [0, 0, 0, 0, 0, 0] cat [(Binomial(n-1, 5))* 120: n in [7..30]]; // Vincenzo Librandi, May 04 2013
(PARI) x='x+O('x^66); concat([0, 0, 0, 0, 0, 0], Vec(serlaplace(x^5*exp(x)-x^5))) \\ Joerg Arndt, May 06 2013

Crossrefs

Sequence in context: A090392 A253734 A112530 * A321842 A052794 A226885

Adjacent sequences: A052797 A052798 A052799 * A052801 A052802 A052803

Keyword

easy,nonn

Author

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

Extensions

More terms from Vincenzo Librandi, May 04 2013

New name using e.g.f., Vaclav Kotesovec, Feb 25 2014

Status

approved