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a(n)=6(2n-4)!/((n-2)!n!), if n>2. a(0)=1,a(1)=a(2)=2.
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%I #3 Apr 30 2014 01:32:50

%S 1,2,2,2,3,6,14,36,99,286,858,2652,8398,27132,89148,297160,1002915,

%T 3421710,11785890,40940460,143291610,504932340,1790214660,6382504440,

%U 22870640910,82334307276,297670187844,1080432533656,3935861372604

%N a(n)=6(2n-4)!/((n-2)!n!), if n>2. a(0)=1,a(1)=a(2)=2.

%F G.f.: ((1+10x-2x^2)+(1-4x)^(3/2))/2. a(n)=6(2n-4)!/((n-2)!n!), if n>2. a(n)=a(n-1)(4n-10)/n, if n>3.

%F G.f. A(x) = (2c(x)-1)^3/c(x)^4 = (1-c(x)x)(1+c(x)x)^3, where c(x) = g.f. for Catalan numbers A000108.

%o (PARI) a(n)=if(n<3,(n>=0)+(n>0),6*(2*n-4)!/n!/(n-2)!)

%o (PARI) a(n)=if(n<0,0,polcoeff(((1+10*x-2*x^2)+(1-4*x)*sqrt(1-4*x+x*O(x^n)))/2,n))

%o (PARI) a(n)=if(n<=0,n==0,polcoeff(subst((1-x)*(1+x)^3,x,serreverse(x-x^2+x*O(x^n))),n))

%Y A007054(n)=a(n+2), if n>0.

%Y Essentially the same as A007054.

%K nonn

%O 0,2

%A _Michael Somos_, Jan 31 2004