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A052744 E.g.f. x*(1-2*x-2*x^2-sqrt(1-4*x-4*x^2))/ (2*(1+x)^2).

%I A052744 #20 Jan 30 2020 21:29:14
%S A052744 0,0,0,6,48,840,17280,448560,13789440,491702400,19929369600,
%T A052744 904873939200,45486949939200,2507639957222400,150419515915468800,
%U A052744 9752720435377920000,679630757528346624000,50655177765863903232000
%N A052744 E.g.f. x*(1-2*x-2*x^2-sqrt(1-4*x-4*x^2))/ (2*(1+x)^2).
%H A052744 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=700">Encyclopedia of Combinatorial Structures 700</a>
%F A052744 D-finite with recurrence: a(1)=0, a(2)=0, a(3)=6, (-4*n^4-24*n-24*n^3-44*n^2)*a(n) +(-8*n^3-42*n^2-12-58*n)*a(n+1) +(-3*n^2-8*n+3)*a(n+2) +(n+2)*a(n+3)=0, a(4)=48, a(5)=840, a(6)=17280.
%F A052744 a(n) ~ sqrt(58-41*sqrt(2))*(1+sqrt(2))^(n-1)*2^n*n^(n-1)*exp(-n). - _Vaclav Kotesovec_, Aug 18 2013
%F A052744 a(n)= n!*A052705(n-1). - _R. J. Mathar_, Oct 26 2013
%p A052744 spec := [S,{B=Prod(C,C),S=Prod(B,Z),C=Union(B,S,Z)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%K A052744 easy,nonn
%O A052744 0,4
%A A052744 encyclopedia(AT)pommard.inria.fr, Jan 25 2000