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A210525 G.f.: A(x) = Sum_{n>=0} x^n * A(n*x) * A(-n*x).

%I A210525 #9 Jan 04 2025 19:12:19
%S A210525 1,1,1,2,5,17,129,823,16549,203762,9057969,229117047,20251050469,
%T A210525 1099941609906,182745344595201,21826976698036317,6625997170286326085,
%U A210525 1760792727174811634066,963263479575497024110193,572732462137043288595101258,560867188756075075604736149189
%N A210525 G.f.: A(x) = Sum_{n>=0} x^n * A(n*x) * A(-n*x).
%e A210525 G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 17*x^5 + 129*x^6 + 823*x^7 +...
%e A210525 such that
%e A210525 A(x) = 1 + x*A(x)*A(-x) + x^2*A(2*x)*A(-2*x) + x^3*A(3*x)*A(-3*x) + x^4*A(4*x)*A(-4*x) + x^5*A(5*x)*A(-5*x) +...
%e A210525 where
%e A210525 A(x)*A(-x) = 1 + x^2 + 7*x^4 + 230*x^6 + 31667*x^8 + 17739221*x^10 + 40061321883*x^12 + 363330478847435*x^14 +...
%o A210525 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=sum(k=0, n, x^k*subst(A,x,k*x +x*O(x^n))*subst(A,x,-k*x +x*O(x^n)))  );polcoeff(A, n)}
%o A210525 for(n=0, 30, print1(a(n), ", "))
%Y A210525 Cf. A125282, A196196.
%K A210525 nonn
%O A210525 0,4
%A A210525 _Paul D. Hanna_, Jan 27 2013