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A052742 A simple context-free grammar in a labeled universe. 0

%I #18 Apr 18 2017 07:04:04

%S 0,0,2,12,144,2640,64800,1985760,72817920,3105527040,150907276800,

%T 8226772646400,497068582348800,32962398345676800,2379770152465305600,

%U 185792734381782528000,15595576381312671744000,1400555897449216155648000,133983477830143785811968000,13602115002476999012990976000

%N A simple context-free grammar in a labeled universe.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=698">Encyclopedia of Combinatorial Structures 698</a>

%F E.g.f.: (1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x

%F Recurrence: {a(1)=0, a(2)=2, a(3)=12, (-4*n+n^2-4+n^3)*a(n) +(-6*n^2+6-9*n)*a(n+1) +(n+1)*a(n+2) =0.

%F a(n) ~ sqrt(3/sqrt(2)-2)*n^(n-1)*(3+2*sqrt(2))^(n-1)/exp(n). - _Vaclav Kotesovec_, Oct 05 2013

%F a(n) = n!*A006318(n-2). - _R. J. Mathar_, Oct 18 2013

%p spec := [S,{B=Prod(C,C),C=Union(B,S,Z),S=Prod(Z,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20); # end of program

%p 0,0,seq(simplify(2*n!*hypergeom([ 3-n, n], [2], -1)), n=2..20); # _Mark van Hoeij_, May 29 2013

%t CoefficientList[Series[(1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 05 2013 *)

%o (PARI) x='x+O('x^66); concat([0,0], Vec( serlaplace( (1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x))) \\ _Joerg Arndt_, May 29 2013

%K easy,nonn

%O 0,3

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

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)