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A213281 G.f. satisfies: A(x) = 1 + x/A(-x)^3.

%I A213281 #14 Jun 09 2012 04:14:27
%S A213281 1,1,3,-3,-35,48,693,-1046,-16635,26328,442396,-720327,-12541509,
%T A213281 20810208,371430414,-624691212,-11356013899,19293440712,355703260500,
%U A213281 -609103135196,-11355804637164,19568456886336,368147199241021,-637674031240302,-12087185276792061
%N A213281 G.f. satisfies: A(x) = 1 + x/A(-x)^3.
%H A213281 Paul D. Hanna, <a href="/A213281/b213281.txt">Table of n, a(n) for n = 0..100</a>
%F A213281 G.f. satisfies: A(x) = G(x/A(x)^3) where G(x) = A(x*G(x)^3) is the g.f. of A213282.
%F A213281 G.f. satisfies: A(x) = ( x/Series_Reversion( x*F(x/(1-x)^3)^3 ) )^(1/3) where F(x) = 1 + x*F(x)^3 is the g.f. of A001764.
%F A213281 G.f. satisfies: A(x) = A(x)*A(-x) + x/A(x)^2.
%e A213281 G.f.: A(x) = 1 + x + 3*x^2 - 3*x^3 - 35*x^4 + 48*x^5 + 693*x^6 - 1046*x^7 +...
%e A213281 where
%e A213281 1/A(-x) = 1 + x - 2*x^2 - 8*x^3 + 30*x^4 + 143*x^5 - 638*x^6 - 3272*x^7 +...
%e A213281 x/A(-x)^3 = x + 3*x^2 - 3*x^3 - 35*x^4 + 48*x^5 + 693*x^6 - 1046*x^7 +...
%e A213281 A(x)^3 = 1 + 3*x + 12*x^2 + 10*x^3 - 87*x^4 - 102*x^5 + 1632*x^6 + 1974*x^7 +...
%e A213281 The g.f. G(x) of A213282 begins:
%e A213281 G(x) = 1 + x + 6*x^2 + 36*x^3 + 236*x^4 + 1656*x^5 + 12192*x^6 + 92960*x^7 +...
%e A213281 where G(x) = A(x*G(x)^3) and G(x/A(x)^3) = A(x);
%e A213281 also, G(x) = F(x/(1-x)^3) where F(x) = 1 + x*F(x)^3 is g.f. of A001764:
%e A213281 G(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...
%o A213281 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+x/subst(A^3,x,-x+x*O(x^n)));polcoeff(A,n)}
%o A213281 for(n=0,40,print1(a(n),", "))
%Y A213281 Cf. A213282, A213252, A213335; A001764.
%K A213281 sign
%O A213281 0,3
%A A213281 _Paul D. Hanna_, Jun 08 2012