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A213335 G.f. satisfies: A(x) = 1 + x/A(-x)^4.

%I A213335 #12 Jun 09 2012 14:57:42
%S A213335 1,1,4,-6,-84,171,2940,-6576,-124260,291321,5810120,-14012244,
%T A213335 -289392508,711239741,15052561056,-37498302048,-808073773572,
%U A213335 2033589755205,44436219882252,-112715767473482,-2490257138332712,6356863001632326,141706826771491368
%N A213335 G.f. satisfies: A(x) = 1 + x/A(-x)^4.
%H A213335 Paul D. Hanna, <a href="/A213335/b213335.txt">Table of n, a(n) for n = 0..100</a>
%F A213335 G.f. satisfies: A(x) = G(x/A(x)^4) where G(x) = A(x*G(x)^4) is the g.f. of A213336.
%F A213335 G.f. satisfies: A(x) = ( x/Series_Reversion( x*F(x/(1-x)^4)^4 ) )^(1/4) where F(x) = 1 + x*F(x)^4 is the g.f. of A002293.
%F A213335 G.f. satisfies: A(x) = A(x)*A(-x) + x/A(x)^3.
%e A213335 G.f.: A(x) = 1 + x + 4*x^2 - 6*x^3 - 84*x^4 + 171*x^5 + 2940*x^6 - 6576*x^7 +...
%e A213335 where
%e A213335 1/A(-x) = 1 + x - 3*x^2 - 13*x^3 + 77*x^4 + 402*x^5 - 2849*x^6 - 16040*x^7 +...
%e A213335 1/A(-x)^4 = 1 + 4*x - 6*x^2 - 84*x^3 + 171*x^4 + 2940*x^5 - 6576*x^6 +...
%e A213335 A(x)^4 = 1 + 4*x + 22*x^2 + 28*x^3 - 263*x^4 - 476*x^5 + 8740*x^6 +...
%e A213335 The g.f. G(x) of A213336 begins:
%e A213335 G(x) = 1 + x + 8*x^2 + 64*x^3 + 568*x^4 + 5440*x^5 + 54888*x^6 +...
%e A213335 where G(x) = A(x*G(x)^4) and G(x/A(x)^4) = A(x);
%e A213335 also, G(x) = F(x/(1-x)^4) where F(x) = 1 + x*F(x)^4 is g.f. of A002293:
%e A213335 F(x) = 1 + x + 4*x^2 + 22*x^3 + 140*x^4 + 969*x^5 + 7084*x^6 +...
%o A213335 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x/subst(A^4, x, -x+x*O(x^n))); polcoeff(A, n)}
%o A213335 for(n=0, 40, print1(a(n), ", "))
%Y A213335 Cf. A213336, A213252, A213281, A143047; A002293.
%K A213335 sign
%O A213335 0,3
%A A213335 _Paul D. Hanna_, Jun 09 2012