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%I #17 Jun 14 2022 01:44:45
%S 0,0,2,24,384,7680,184320,5160960,165150720,5945425920,237817036800,
%T 10463949619200,502269581721600,26118018249523200,1462609021973299200,
%U 87756541318397952000,5616418644377468928000
%N Expansion of e.g.f. x^2/(1-4*x).
%H G. C. Greubel, <a href="/A052670/b052670.txt">Table of n, a(n) for n = 0..350</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=618">Encyclopedia of Combinatorial Structures 618</a>
%F E.g.f.: x^2/(1 - 4*x)
%F Recurrence: a(0)=0, a(1)=0, a(2)=2, a(n) = 4*n*a(n-1).
%F a(n) = 4^(n-2) * n!, n>1.
%F G.f.: 2*x^2*Hypergeometric2F0([3,1], [], 4*x). - _G. C. Greubel_, Jun 13 2022
%p spec := [S,{S=Prod(Z,Z,Sequence(Union(Z,Z,Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[x^2/(1-4x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 27 2015 *)
%o (Magma) [0,0] cat [4^(n-2)*Factorial(n): n in [2..30]]; // _G. C. Greubel_, Jun 13 2022
%o (SageMath) [(4^(n-2) - 4^(n-2)*bool(n<2))*factorial(n) for n in (0..30)] # _G. C. Greubel_, Jun 13 2022
%Y Cf. A000142, A000302.
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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