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A276366 G.f. A(x) satisfies: A(x - A(x)^3) = x + A(x)^2.

%I A276366 #14 Mar 10 2023 07:41:41
%S A276366 1,1,3,12,57,300,1697,10126,62991,405247,2680901,18160444,125562250,
%T A276366 883868590,6321838520,45869309028,337167193262,2508018933431,
%U A276366 18861358215299,143293615189089,1098997404472941,8504070741463729,66358269984208701,521923129718567918,4136089275165532156,33013640650845937124
%N A276366 G.f. A(x) satisfies: A(x - A(x)^3) = x + A(x)^2.
%H A276366 Paul D. Hanna, <a href="/A276366/b276366.txt">Table of n, a(n) for n = 1..300</a>
%F A276366 G.f. A(x) satisfies: A'(x - A(x)^3) = (1 + 2*A'(x)*A(x)) / (1 - 3*A'(x)*A(x)^2).
%e A276366 G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 57*x^5 + 300*x^6 + 1697*x^7 + 10126*x^8 + 62991*x^9 + 405247*x^10 + 2680901*x^11 + 18160444*x^12 +...
%e A276366 such that A(x - A(x)^3) = x + A(x)^2.
%e A276366 RELATED SERIES.
%e A276366 A(x - A(x)^3) = x + x^2 + 2*x^3 + 7*x^4 + 30*x^5 + 147*x^6 + 786*x^7 + 4480*x^8 + 26814*x^9 + 166865*x^10 + 1072160*x^11 + 7076724*x^12 +...
%e A276366 which equals x + A(x)^2.
%o A276366 (PARI) {a(n) = my(A=[1], F=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = -polcoeff(subst(F, x, x-F^3) - F^2, #A) ); A[n]}
%o A276366 for(n=1, 30, print1(a(n), ", "))
%Y A276366 Cf. A153851, A275765, A276364.
%K A276366 nonn
%O A276366 1,3
%A A276366 _Paul D. Hanna_, Sep 01 2016