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%I #6 Jul 21 2014 19:06:22
%S 1,1,2,10,77,771,9258,127656,1969366,33422650,616779303,12272428173,
%T 261620716744,5945330149226,143439343672519,3661506704040203,
%U 98597706579694403,2793561790527733313,83084652845766283317,2588418449175558698525,84305591450606402889544
%N G.f. satisfies: A(x) = A( x/A(x) )^2 / (1+x).
%e G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 77*x^4 + 771*x^5 + 9258*x^6 +...
%e Related expansions.
%e A(x)^2 = 1 + 2*x + 5*x^2 + 24*x^3 + 178*x^4 + 1736*x^5 + 20466*x^6 +...
%e A(x/A(x))^2 = 1 + 2*x + 3*x^2 + 12*x^3 + 87*x^4 + 848*x^5 + 10029*x^6 +...
%e A(x/A(x)) = 1 + x + x^2 + 5*x^3 + 38*x^4 + 381*x^5 + 4583*x^6 + 63303*x^7 + 977998*x^8 + 16617314*x^9 + 306942415*x^10 +...
%o (PARI) {a(n)=local(A=[1,1]);for(i=1,n,A=concat(A,0);(A[#A]=-Vec(subst(Ser(A)^2,x,x/Ser(A))/(1+x))[#A]));A[n+1]}
%o for(n=0,30,print1(a(n),", "))
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 21 2014
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