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%I #3 Mar 30 2012 18:36:58
%S 1,1,3,8,27,89,300,1008,3563,12483,44583,158600,572548,2057792,
%T 7451924,26913176,98321435,358017691,1312060393,4797471336,
%U 17666696455,64890598361,239454075896,881886659872,3264772507980,12061404124676
%N A bisection of A121649; a(n) = A121649(2*n) = A121648(2*n)^(1/2).
%F G.f.: A(x) = 1/(1 - x*B(x)^2), where B(x) = Sum_{n>=0} A121649(n)^2*x^n is the g.f. of A121648.
%e A(x) = 1 + x + 3*x^2 + 8*x^3 + 27*x^4 + 89*x^5 + 300*x^6 +...
%e 1/A(x) = 1 - x - 2*x^2 - 3*x^3 - 10*x^4 - 27*x^5 - 76*x^6 - 212*x^7 -...
%e 1/A(x) = 1 - x*B(x)^2, where
%e B(x)^2 = 1 + 2*x + 3*x^2 + 10*x^3 + 27*x^4 + 76*x^5 + 212*x^6 +...
%e and B(x) is the g.f. of A121648 where all coefficients are squares:
%e B(x) = 1 + x + x^2 + 4*x^3 + 9*x^4 + 25*x^5 + 64*x^6 + 256*x^7 +...
%o (PARI) {a(n)=local(B=1+x);if(n==0, 1, for(m=0,n,B=1/(1-x*sum(k=0,m,polcoeff(B,k)^2*x^(2*k))+O(x^(2*n+2)))); polcoeff(B,2*n))}
%Y Cf. A121648, A121649, A121651.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 14 2006
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