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A277305 G.f. satisfies: A(x - 5*A(x)^2) = x + A(x)^2.

%I A277305 #9 Oct 25 2016 21:20:00
%S A277305 1,6,132,4350,176964,8235252,421814232,23252672574,1359954622860,
%T A277305 83572511671092,5359130778285096,356786692299782916,
%U A277305 24565803644793789192,1744056102774572824920,127369971591949093219920,9550397045409732902387790,734084078724419876468356500,57766855968717521513179054860,4648888743682938087701732224680
%N A277305 G.f. satisfies: A(x - 5*A(x)^2) = x + A(x)^2.
%H A277305 Paul D. Hanna, <a href="/A277305/b277305.txt">Table of n, a(n) for n = 1..300</a>
%F A277305 G.f. A(x) also satisfies:
%F A277305 (1) A(x) = x + 6 * A( x/6 + 5*A(x)/6 )^2.
%F A277305 (2) A(x) = -x/5 + 6/5 * Series_Reversion(x - 5*A(x)^2).
%F A277305 (3) R(x) = -5*x + 6 * Series_Reversion(x + A(x)^2), where R(A(x)) = x.
%F A277305 (4) R( sqrt( x/6 - R(x)/6 ) ) = 5*x/6 + R(x)/6, where R(A(x)) = x.
%F A277305 a(n) = Sum_{k=0..n-1} A277295(n,k) * 5^k * 6^(n-k-1).
%e A277305 G.f.: A(x) = x + 6*x^2 + 132*x^3 + 4350*x^4 + 176964*x^5 + 8235252*x^6 + 421814232*x^7 + 23252672574*x^8 + 1359954622860*x^9 + 83572511671092*x^10 +...
%o A277305 (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 - 5*F^2) - F^2, #A) ); A[n]}
%o A277305 for(n=1, 30, print1(a(n), ", "))
%Y A277305 Cf. A277295, A213591, A275765, A276360, A276361, A276362, A276363.
%Y A277305 Cf. A277300, A277301, A277302, A277303, A277304, A277306, A277307, A277308, A277309.
%Y A277305 Cf. A276364.
%K A277305 nonn
%O A277305 1,2
%A A277305 _Paul D. Hanna_, Oct 09 2016