%I #19 Jun 04 2022 01:44:41

%S 0,0,0,0,48,240,1440,10080,80640,725760,7257600,79833600,958003200,

%T 12454041600,174356582400,2615348736000,41845579776000,

%U 711374856192000,12804747411456000,243290200817664000

%N Expansion of e.g.f. 2*x^4/(1-x).

%H G. C. Greubel, <a href="/A052683/b052683.txt">Table of n, a(n) for n = 0..350</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=631">Encyclopedia of Combinatorial Structures 631</a>

%F E.g.f.: 2*x^4/(1-x)

%F D-finite recurrence: a(n)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=48, a(n) = n*a(n-1).

%F a(n) = 2*n!, n>3.

%F G.f.: 48*x^4*hypergeometric2F0([1,5], [], x). - _G. C. Greubel_, Jun 04 2022

%p spec := [S,{S=Prod(Z,Z,Z,Sequence(Z),Union(Z,Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%t With[{nn=20},CoefficientList[Series[(2x^4)/(1-x),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, May 22 2012 *)

%t Table[2*n!*(1-Boole[n<4]), {n,0,40}] (* _G. C. Greubel_, Jun 04 2022 *)

%o (Magma) [n le 3 select 0 else 2*Factorial(n): n in [0..40]]; // _G. C. Greubel_, Jun 04 2022

%o (SageMath) [2*factorial(n)*(1 - bool(n<4)) for n in (0..40)] # _G. C. Greubel_, Jun 04 2022

%Y Cf. A000142.

%K easy,nonn

%O 0,5

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