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 A213628 G.f. satisfies: A(x) = 1 - (x^2/A(x)) / A( x^2/A(x) ). 3

%I

%S 1,1,3,14,85,616,5072,46013,450739,4702265,51731956,595874703,

%T 7147366614,88905147730,1143097097833,15152617826426,206646826047563,

%U 2894398418226395,41577147999077079,611779190051375147,9211548488261257610,141802624561414800815

%N G.f. satisfies: A(x) = 1 - (x^2/A(x)) / A( x^2/A(x) ).

%F G.f.: A(x) = x^2/(x - G(x)^2) where G(x) is the g.f. of A213591 such that G(x^2/A(x)) = G(x - G(x)^2) = x.

%F G.f.: A(x) = Series_Reversion(x*F(x)) where F(x) = 1 + x*F(1 - 1/F(x))^2 is the g.f. of A212411.

%e G.f.: A(x) = x + x^2 + 3*x^3 + 14*x^4 + 85*x^5 + 616*x^6 + 5072*x^7 +...

%e Related expansions:

%e x^2/A(x) = x - x^2 - 2*x^3 - 9*x^4 - 56*x^5 - 420*x^6 - 3572*x^7 -...

%e A(x^2/A(x)) = x - x^3 - 7*x^4 - 50*x^5 - 395*x^6 - 3436*x^7 -...

%e A(x) = x^2/Series_Reversion(G(x)) where G(x) is the g.f. of A213591:

%e G(x) = x + x^2 + 4*x^3 + 24*x^4 + 178*x^5 + 1512*x^6 + 14152*x^7 +...

%e such that G(x - G(x)^2) = x.

%o (PARI) {a(n)=local(A=x,G=x); if(n<1, 0, for(i=1, n, G=serreverse(x - G^2+x*O(x^n)));A=x^2/(x-G^2);polcoeff(A, n))}

%o for(n=1,25,print1(a(n),", "))

%Y Cf. A213591, A212411.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jun 16 2012

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)