A052724 A simple context-free grammar in a labeled universe: a(n) = A052743(n)-A052723(n), n>1.
0, 0, 0, 0, 24, 240, 2160, 30240, 524160, 9434880, 188697600, 4311014400, 108254361600, 2939153817600, 86568043161600, 2753962219008000, 93838712647680000, 3409619685728256000, 131735241369059328000
Offset: 0
Links
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 680
Programs
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Maple
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); 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
Formula
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
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}
a(n) = n!*A052702(n). - R. J. Mathar, Oct 18 2013