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 A277309 #9 Oct 25 2016 21:24:18
%S A277309 1,2,28,570,14284,410604,13046728,448252682,16417945620,634848045084,
%T A277309 25737059674104,1088311917852828,47813839403065432,
%U A277309 2175881570186952520,102316326149365110320,4961686220242926811690,247733650768933667153660,12718117037478356041212500,670565414769224589112024760,36274908884974158393988101900,2011581759381610503724213971960
%N A277309 G.f. satisfies: A(x - 5*A(x)^2) = x - 3*A(x)^2.
%H A277309 Paul D. Hanna, <a href="/A277309/b277309.txt">Table of n, a(n) for n = 1..300</a>
%F A277309 G.f. A(x) also satisfies:
%F A277309 (1) A(x) = x + 2 * A( 5*A(x)/2 - 3*x/2 )^2.
%F A277309 (2) A(x) = 3*x/5 + 2/5 * Series_Reversion(x - 5*A(x)^2).
%F A277309 (3) R(x) = 5*x/3 - 2/3 * Series_Reversion(x - 3*A(x)^2), where R(A(x)) = x.
%F A277309 (4) R( sqrt( x/2 - R(x)/2 ) ) = 5*x/2 - 3*R(x)/2, where R(A(x)) = x.
%F A277309 a(n) = Sum_{k=0..n-1} A277295(n,k) * 5^k * 2^(n-k-1).
%e A277309 G.f.: A(x) = x + 2*x^2 + 28*x^3 + 570*x^4 + 14284*x^5 + 410604*x^6 + 13046728*x^7 + 448252682*x^8 + 16417945620*x^9 + 634848045084*x^10 +...
%o A277309 (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) + 3*F^2, #A) ); A[n]}
%o A277309 for(n=1, 30, print1(a(n), ", "))
%Y A277309 Cf. A277295, A213591, A275765, A276360, A276361, A276362, A276363.
%Y A277309 Cf. A277300, A277301, A277302, A277303, A277304, A277305, A277306, A277307, A277308.
%Y A277309 Cf. A276364.
%K A277309 nonn
%O A277309 1,2
%A A277309 _Paul D. Hanna_, Oct 09 2016