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A052724 A simple context-free grammar in a labeled universe: a(n) = A052743(n)-A052723(n), n>1.

%I A052724 #18 Jan 13 2025 10:24:01
%S A052724 0,0,0,0,24,240,2160,30240,524160,9434880,188697600,4311014400,
%T A052724 108254361600,2939153817600,86568043161600,2753962219008000,
%U A052724 93838712647680000,3409619685728256000,131735241369059328000
%N A052724 A simple context-free grammar in a labeled universe: a(n) = A052743(n)-A052723(n), n>1.
%H A052724 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=680">Encyclopedia of Combinatorial Structures 680</a>
%F A052724 E.g.f.: (1/2)/x^2*(1-x-(1-2*x+x^2-4*x^3)^(1/2))-(1/2)/x*(1-x-(1-2*x+x^2-4*x^3)^(1/2))-x
%F A052724 Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, a(6)=2160, a(7)=30240, (38*n^4+120*n^3-48-4*n+130*n^2+4*n^5)*a(n) +(-193*n^2-52*n^3-302*n-5*n^4-168)*a(n+1) +(96+29*n^2+92*n+3*n^3)*a(n+2) +(-52-3*n^2-25*n)*a(n+3) +(n+6)*a(n+4)=0, a(5)=240}
%F A052724 a(n) = n!*A052702(n). - _R. J. Mathar_, Oct 18 2013
%p A052724 spec := [S,{B=Prod(Z,C),C=Union(B,S,Z),S=Prod(B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p A052724 seq(n!*add(binomial(n-k-2, 2*k-1)*binomial(2*k, k)/(k+1), k=0..n-2), n=0..20);  # _Mark van Hoeij_, May 12 2013
%K A052724 easy,nonn
%O A052724 0,5
%A A052724 encyclopedia(AT)pommard.inria.fr, Jan 25 2000