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%I A052683 #19 Jun 04 2022 01:44:41
%S A052683 0,0,0,0,48,240,1440,10080,80640,725760,7257600,79833600,958003200,
%T A052683 12454041600,174356582400,2615348736000,41845579776000,
%U A052683 711374856192000,12804747411456000,243290200817664000
%N A052683 Expansion of e.g.f. 2*x^4/(1-x).
%H A052683 G. C. Greubel, <a href="/A052683/b052683.txt">Table of n, a(n) for n = 0..350</a>
%H A052683 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=631">Encyclopedia of Combinatorial Structures 631</a>
%F A052683 E.g.f.: 2*x^4/(1-x)
%F A052683 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 A052683 a(n) = 2*n!, n>3.
%F A052683 G.f.: 48*x^4*hypergeometric2F0([1,5], [], x). - _G. C. Greubel_, Jun 04 2022
%p A052683 spec := [S,{S=Prod(Z,Z,Z,Sequence(Z),Union(Z,Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052683 With[{nn=20},CoefficientList[Series[(2x^4)/(1-x),{x,0,nn}],x] Range[ 0,nn]!]  (* _Harvey P. Dale_, May 22 2012 *)
%t A052683 Table[2*n!*(1-Boole[n<4]), {n,0,40}] (* _G. C. Greubel_, Jun 04 2022 *)
%o A052683 (Magma) [n le 3 select 0 else 2*Factorial(n): n in [0..40]]; // _G. C. Greubel_, Jun 04 2022
%o A052683 (SageMath) [2*factorial(n)*(1 - bool(n<4)) for n in (0..40)] # _G. C. Greubel_, Jun 04 2022
%Y A052683 Cf. A000142.
%K A052683 easy,nonn
%O A052683 0,5
%A A052683 encyclopedia(AT)pommard.inria.fr, Jan 25 2000

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