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A107099 G.f. satisfies A(A(x)) = x + 4*x^3, where A(x) = Sum_{n>=0} a(n)*x^(2*n+1).

%I A107099 #11 May 04 2024 09:26:28
%S A107099 1,2,-6,36,-266,2028,-13596,50088,566694,-16598580,232284876,
%T A107099 -1912070088,631155132,239439857272,-2781218767224,-17362458802992,
%U A107099 795693633448710,-458070639409908,-335724554310292548,4520379769156382616,109439050270732883028,-3828757746830590219608
%N A107099 G.f. satisfies A(A(x)) = x + 4*x^3, where A(x) = Sum_{n>=0} a(n)*x^(2*n+1).
%C A107099 Coefficients [x^n] A(x) = 0 (mod 3) except at n = 3^k (conjecture).
%H A107099 Seiichi Manyama, <a href="/A107099/b107099.txt">Table of n, a(n) for n = 0..433</a>
%e A107099 A(x) = 1*x + 2*x^3 - 6*x^5 + 36*x^7 - 266*x^9 + 2028*x^11 - 13596*x^13 +-...
%o A107099 (PARI) b(n) = local(A,B,F);F=x+4*x^3+x*O(x^n);A=F;if(n==0,0, for(i=0,n,B=serreverse(A);A=(A+subst(B,x,F))/2);polcoeff(A,n,x));
%o A107099 a(n) = b(2*n+1);
%Y A107099 Cf. A027436, A097090.
%K A107099 sign
%O A107099 0,2
%A A107099 _Paul D. Hanna_, May 13 2005