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%I #3 Mar 30 2012 18:36:59
%S 1,2,3,6,17,70,390,2776,24042,244864,2862185,37715474,552685976,
%T 8910951840,156709821779,2984589501562,61188398397436,
%U 1343410717573876,31445844702847347,781689483100388326,20564696601659697997
%N G.f. A(x) satisfies: A(x+x^2) = A(x)^2/(1+x)^2.
%C Self-convolution of A122938. See A122888 for the table of self-compositions of x+x^2.
%F G.f.: A(x) = Product_{n>=0} (1 + F_n(x) )^(1/2^n) where F_0(x)=x, F_{n+1}(x)=F_n(x+x^2); a product that involves the n-th self-compositions of x+x^2.
%e G.f.: A(x) = (1 + x) * (1 + x+x^2)^(1/2) * (1 + x+2x^2+2x^3+x^4)^(1/4) * (1 + x+3x^2+6x^3+9x^4+10x^5+8x^6+4x^7+x^8)^(1/8) *...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0,n,A=-A+2*(1+x)*sqrt(subst(A,x,x+x^2+x*O(x^n))));polcoeff(A,n)}
%Y Cf. A122938 (square-root), A122888 (table).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Sep 21 2006
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