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%I #2 Mar 30 2012 18:37:16
%S 1,1,2,5,15,50,177,649,2437,9322,36214,142546,567409,2280246,9238883,
%T 37699021,154783906,638983998,2650697658,11043733080,46192300706,
%U 193892210528,816486626337,3448376227978,14603301098654,61996178908151
%N G.f. satisfies: A(x) = Sum_{n>=0} x^(n^2) * A(x)^(n^2+n).
%F G.f. satisfies: A(x) = B(x*A(x)) where B(x) = A(x/B(x)) = g.f. of A157134,
%F where A157134(n) = [x^n] -1/A(x)^(n-1)/(n-1) for n>1,
%F and a(n) = [x^n] B(x)^(n+1)/(n+1) for n>=0.
%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 50*x^5 + 177*x^6 +...
%e A(x)^2 = 1 + 2*x + 5*x^2 + 14*x^3 + 44*x^4 + 150*x^5 + 539*x^6 +...
%e A(x)^6 = 1 + 6*x + 27*x^2 + 110*x^3 + 435*x^4 + 1716*x^5 +...
%e A(x)^12 = 1 + 12*x + 90*x^2 + 544*x^3 + 2919*x^4 + 14592*x^5 +...
%e where
%e A(x) = 1 + x*A(x)^2 + x^4*A(x)^6 + x^9*A(x)^12 + x^16*A(x)^20 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,(A=sum(m=0,sqrtint(n),x^(m^2)*A^(m*(m+1)))));polcoeff(A,n)}
%Y Cf. A157134, A157133, A157136.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Feb 24 2009
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