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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A212411 G.f. satisfies: A(x) = 1 + x*A(1 - 1/A(x))^2.

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%I A212411 #13 Jun 22 2012 00:10:42
%S A212411 1,1,2,7,36,235,1792,15261,141382,1401334,14694166,161714217,
%T A212411 1857003186,22152227989,273573165626,3488210643709,45820081884234,
%U A212411 618950367384072,8585324020132250,122127635117014779,1779763238159032068,26545963246376545934
%N A212411 G.f. satisfies: A(x) = 1 + x*A(1 - 1/A(x))^2.
%C A212411 Compare g.f. to the identity: G(x) = 1 + x*G(1-1/G(x)) when G(x) = 1/(1-x).
%H A212411 Vincenzo Librandi, <a href="/A212411/b212411.txt">Table of n, a(n) for n = 0..100</a>
%F A212411 Given g.f. A(x), let G(x) be the g.f. of A213591, then:
%F A212411 (1) G(x) = x*A(G(x)^2/x),
%F A212411 (2) A( x/(1 - G(x)^2/x) ) = 1/(1 - G(x)^2/x),
%F A212411 (3) x = G(x - G(x)^2).
%F A212411 G.f.: A(x) = x/Series_Reversion(F(x)) where F(x) = 1 - (x^2/F(x))/F(x^2/F(x)) is the g.f. of A213628.
%F A212411 Given g.f. A(x), let F(x) = A(1-1/A(x)), then F(1-1/A(x)) = A(1-1/F(x)) and A(x) = 1 + x*F(x)^2.
%e A212411 G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 36*x^4 + 235*x^5 + 1792*x^6 +...
%e A212411 Related expansions:
%e A212411 A(x)^2 = 1 + 2*x + 5*x^2 + 18*x^3 + 90*x^4 + 570*x^5 + 4247*x^6 +...
%e A212411 1 - 1/A(x) = x + x^2 + 4*x^3 + 23*x^4 + 161*x^5 + 1286*x^6 + 11321*x^7 +...
%e A212411 A(1-1/A(x)) = 1 + x + 3*x^2 + 15*x^3 + 98*x^4 + 753*x^5 + 6471*x^6 +...
%e A212411 Let F(x) = A(1-1/A(x)), then F(1-1/A(x)) = A(1-1/F(x)):
%e A212411 F(1-1/A(x)) = 1 + x + 4*x^2 + 25*x^3 + 193*x^4 + 1693*x^5 + 16240*x^6 +...
%e A212411 ...
%e A212411 Let G(x) be the g.f. of A213591, then
%e A212411 G(x) satisfies: x = G(x - G(x)^2) and G(x) = A(G(x)^2/x), where:
%e A212411 G(x) = x + x^2 + 4*x^3 + 24*x^4 + 178*x^5 + 1512*x^6 + 14152*x^7 +...
%e A212411 G(x)^2/x = x + 2*x^2 + 9*x^3 + 56*x^4 + 420*x^5 + 3572*x^6 +...
%e A212411 1/(1-G(x)^2/x) = 1 + x + 3*x^2 + 14*x^3 + 85*x^4 + 616*x^5 + 5072*x^6 +...
%e A212411 such that A(x/(1 - G(x)^2/x)) = 1/(1 - G(x)^2/x).
%o A212411 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+x*subst(A^2,x,1-1/(A+x*O(x^n))));polcoeff(A,n)}
%o A212411 for(n=0,30,print1(a(n),", "))
%Y A212411 Cf. A213591, A213628.
%K A212411 nonn
%O A212411 0,3
%A A212411 _Paul D. Hanna_, May 15 2012