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%I #20 Jun 01 2022 09:43:40
%S 2,5,34,390,6168,123000,2949840,82580400,2642451840,95127177600,
%T 3805076217600,167423233824000,8036313786547200,417888298219392000,
%U 23401744438751078400,1404104662402041600000,89862698330962292736000
%N Expansion of e.g.f. (2-5*x)/((1-x)*(1-4*x)).
%H G. C. Greubel, <a href="/A052695/b052695.txt">Table of n, a(n) for n = 0..360</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=644">Encyclopedia of Combinatorial Structures 644</a>
%F E.g.f.: (2-5*x)/((1-x)*(1-4*x)).
%F D-finite Recurrence: a(0)=2, a(1)=5, a(n) = 5*n*a(n-1) - 4*n*(n-1)*a(n-2).
%F a(n) = (4^n + 1)*n!.
%p spec := [S,{S=Union(Sequence(Z),Sequence(Union(Z,Z,Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[(2-5x)/((1-4x)(1-x)),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Sep 12 2020 *)
%o (SageMath) [factorial(n)*(4^n +1) for n in (0..30)] # _G. C. Greubel_, May 31 2022
%Y Cf. A000142, A052539.
%K easy,nonn
%O 0,1
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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