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%I #3 Mar 30 2012 18:36:58
%S 1,1,2,-7,-58,369,4572,-40188,-618694,6915257,123744242,-1683380975,
%T -34017509348,546799381140,12298020900128,-228437416454904,
%U -5666681561083638,119532757362516473,3247637352945151374,-76715605444589999941,-2268946268485834353378
%N G.f. A(x) satisfies the condition that both series_reversion(x/A(x))/x (cf. A120953) and series_reversion(x*A(x))/x (cf. A120954) have zeros for every other coefficient after initial terms.
%F G.f. satisfies: A(x) = G(x/A(x)) where G(x) = g.f. of A120953. G.f. satisfies: A(x) = 1/H(x*A(x)) where H(x) = g.f. of A120954.
%e A(x) = 1 + x + 2*x^2 - 7*x^3 - 58*x^4 + 369*x^5 + 4572*x^6 --++...
%e series_reversion(x/A(x))/x = 1 + x + 3*x^2 - 65*x^4 + 4998*x^6 -+...
%e series_reversion(x*A(x))/x = 1 - x + 12*x^3 - 663*x^5 + 70992*x^7 -+...
%o (PARI) {a(n)=local(A=[1,1]);for(i=1,n, if(#A%2==1,A=concat(A,t);A[ #A]=-subst(Vec(serreverse(x/Ser(A)))[ #A],t,0)); if(#A%2==0,A=concat(A,t);A[ #A]=subst(Vec(serreverse(x*Ser(A)))[ #A],t,0)));A[n+1]}
%Y Cf. A120953, A120954.
%K sign
%O 0,3
%A _Paul D. Hanna_, Jul 19 2006
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