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.
%I A277302 #9 Oct 25 2016 21:14:03
%S A277302 1,5,80,1900,55490,1848660,67630080,2657251005,110560510400,
%T A277302 4824793769260,219334788340040,10334817935549420,502814686712631520,
%U A277302 25184673137026274600,1295595210394570426800,68326193725188929358600,3688253200687778850553800,203524353764195058692833200,11468618360097679305600299400,659345494779348103800864088800,38644445208422874351089132287200
%N A277302 G.f. satisfies: A(x - 3*A(x)^2) = x + 2*A(x)^2.
%H A277302 Paul D. Hanna, <a href="/A277302/b277302.txt">Table of n, a(n) for n = 1..300</a>
%F A277302 G.f. A(x) also satisfies:
%F A277302 (1) A(x) = x + 5 * A( 2*x/5 + 3*A(x)/5 )^2.
%F A277302 (2) A(x) = -2*x/3 + 5/3 * Series_Reversion(x - 3*A(x)^2).
%F A277302 (3) R(x) = -3*x/2 + 5/2 * Series_Reversion(x + 2*A(x)^2), where R(A(x)) = x.
%F A277302 (4) R( sqrt( x/5 - R(x)/5 ) ) = 3*x/5 + 2*R(x)/5, where R(A(x)) = x.
%F A277302 a(n) = Sum_{k=0..n-1} A277295(n,k) * 3^k * 5^(n-k-1).
%e A277302 G.f.: A(x) = x + 5*x^2 + 80*x^3 + 1900*x^4 + 55490*x^5 + 1848660*x^6 + 67630080*x^7 + 2657251005*x^8 + 110560510400*x^9 + 4824793769260*x^10 +...
%o A277302 (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 - 3*F^2) - 2*F^2, #A) ); A[n]}
%o A277302 for(n=1, 30, print1(a(n), ", "))
%Y A277302 Cf. A277295, A213591, A275765, A276360, A276361, A276362, A276363.
%Y A277302 Cf. A277300, A277301, A277303, A277304, A277305, A277306, A277307, A277308, A277309.
%Y A277302 Cf. A276364.
%K A277302 nonn
%O A277302 1,2
%A A277302 _Paul D. Hanna_, Oct 09 2016