A052800 - OEIS

%I #23 Sep 08 2022 08:44:59

%S 0,0,0,0,0,0,720,2520,6720,15120,30240,55440,95040,154440,240240,

%T 360360,524160,742560,1028160,1395360,1860480,2441880,3160080,4037880,

%U 5100480,6375600,7893600,9687600,11793600,14250600,17100720,20389320,24165120

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

%C Previous name was: A simple grammar.

%H Vincenzo Librandi, <a href="/A052800/b052800.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=758">Encyclopedia of Combinatorial Structures 758</a>

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

%F 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)}

%p 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);

%t Flatten[{0,0,0,0,0,0, Table[Binomial[n-1, 5]*5!, {n, 7, 35}]}] (* _Vaclav Kotesovec_, Oct 28 2012 *)

%t CoefficientList[Series[x^5 Exp[x] - x^5, {x, 0, 30}], x] Table[n!, {n, 0, 30} (* _Vincenzo Librandi_, May 04 2013 *)

%o (Magma) [0,0,0,0,0,0] cat [(Binomial(n-1,5))* 120: n in [7..30]]; // _Vincenzo Librandi_, May 04 2013

%o (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

%K easy,nonn

%O 0,7

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

%E More terms from _Vincenzo Librandi_, May 04 2013

%E New name using e.g.f., _Vaclav Kotesovec_, Feb 25 2014