A052740 - OEIS

%I #14 Jun 03 2022 18:18:18

%S 0,1,2,12,144,2400,50400,1290240,39070080,1365154560,54047347200,

%T 2391175987200,116918542540800,6260970517401600,364413626331955200,

%U 22906448213096448000,1546480919558615040000,111605770820457897984000

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

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=696">Encyclopedia of Combinatorial Structures 696</a>

%F E.g.f.: RootOf(-_Z+_Z^4+_Z^2+x)

%F D-finite Recurrence: {a(1)=1, a(0)=0, a(2)=2, a(3)=12, (576*n-9216*n^3-2688*n^2+192-6144*n^4)*a(n) +(-6400*n^3-23112-36480*n^2-54608*n)*a(n+1) +(13184*n+17772+896*n^2)*a(n+2) +(-14800-5176*n)*a(n+3) +1147*a(n+4) =0,.

%F a(n) = n!*A049140(n). - _R. J. Mathar_, Oct 18 2013

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

%K easy,nonn

%O 0,3

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