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A171992 G.f. satisfies: A(x) = x + A(A(x))^2 - A(A(x))^4.

%I A171992 #14 Mar 12 2022 13:10:18
%S A171992 1,1,4,23,166,1380,12684,125857,1328084,14754242,171338020,2069009164,
%T A171992 25877555908,334197713580,4445788022944,60800921601639,
%U A171992 853479846713406,12280659254071964,180929894848439516,2726751302240331150,42001984460083899448,660800371941797598828
%N A171992 G.f. satisfies: A(x) = x + A(A(x))^2 - A(A(x))^4.
%F A171992 G.f. satisfies: A( x - A(x)^2 + A(x)^4 ) = x.
%e A171992 G.f.: A(x) = x + x^2 + 4*x^3 + 23*x^4 + 166*x^5 + 1380*x^6 + 12684*x^7 +...
%e A171992 Related series begin:
%e A171992 A(A(x)) = x + 2*x^2 + 10*x^3 + 67*x^4 + 538*x^5 + 4866*x^6 + 48000*x^7 +...
%e A171992 A(A(x))^2 = x^2 + 4*x^3 + 24*x^4 + 174*x^5 + 1444*x^6 + 13224*x^7 +...
%e A171992 A(A(x))^4 = x^4 + 8*x^5 + 64*x^6 + 540*x^7 + 4856*x^8 + 46352*x^9 +...
%e A171992 A(x)^2 = x^2 + 2*x^3 + 9*x^4 + 54*x^5 + 394*x^6 + 3276*x^7 + 29985*x^8 +...
%e A171992 A(x)^4 = x^4 + 4*x^5 + 22*x^6 + 144*x^7 + 1085*x^8 + 9100*x^9 +...
%e A171992 where the series reversion of the g.f. A(x) begins:
%e A171992 x - A(x)^2 + A(x)^4 = x - x^2 - 2*x^3 - 8*x^4 - 50*x^5 - 372*x^6 - 3132*x^7 -...
%o A171992 (PARI) {a(n)=local(A=x+x^2,B=x); for(i=1, n, B=subst(A,x,A+x*O(x^n));A=x+B^2-B^4); polcoeff(A, n)}
%o A171992 for(n=1, 30, print1(a(n), ", "))
%o A171992 (PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=serreverse(x-A^2+A^4+x*O(x^n))); polcoeff(A, n)}
%o A171992 for(n=1,30,print1(a(n),", "))
%Y A171992 Cf. A190761, A171991, A213591.
%K A171992 nonn
%O A171992 1,3
%A A171992 _Paul D. Hanna_, Jun 27 2012