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%I #16 Jul 25 2023 07:33:05
%S 1,1,-3,-6,35,87,-588,-1578,11511,32223,-245883,-706824,5556564,
%T 16267508,-130617600,-387533058,3161190783,9474886287,-78241316361,
%U -236394953670,1971270824859,5994591989967,-50388913722480,-154052058035736
%N G.f. satisfies A(x) = 1 + x*A(-x)^3.
%H Seiichi Manyama, <a href="/A143046/b143046.txt">Table of n, a(n) for n = 0..500</a>
%F G.f. satisfies: A(x) = 1 + x*(1 - x*A(x)^3)^3.
%F G.f. satisfies: [A(x)^4 + A(-x)^4]/2 = [A(x)^3 + A(-x)^3]/2.
%e G.f.: A(x) = 1 + x - 3*x^2 - 6*x^3 + 35*x^4 + 87*x^5 - 588*x^6 - 1578*x^7 +...
%e where
%e A(x)^3 = 1 + 3*x - 6*x^2 - 35*x^3 + 87*x^4 + 588*x^5 - 1578*x^6 - 11511*x^7 +...
%e A(x)^4 = 1 + 4*x - 6*x^2 - 56*x^3 + 87*x^4 + 1008*x^5 - 1578*x^6 - 20464*x^7 +...
%e Note that a bisection of A^4 equals a bisection of A^3.
%o (PARI) a(n)=local(A=x+x*O(x^n));for(i=0,n,A=1+x*subst(A,x,-x)^3);polcoeff(A,n)
%Y Cf. A143045, A143047, A143048, A143049, A213252, A213281, A213335.
%Y Cf. A171200.
%K sign
%O 0,3
%A _Paul D. Hanna_, Jul 19 2008
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