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 A277301 #9 Oct 25 2016 21:10:12
%S A277301 1,5,70,1425,35410,999210,30855820,1020407105,35642665050,
%T A277301 1302725802510,49490450201460,1944619121474970,78734794663758580,
%U A277301 3275324221277662900,139667810517388712600,6093781146211490413825,271623891311306597652650,12353670814537544856558950,572686428900679117724156900,27036308383662996662940155550,1298856469077709523772645582300
%N A277301 G.f. satisfies: A(x - 2*A(x)^2) = x + 3*A(x)^2.
%H A277301 Paul D. Hanna, <a href="/A277301/b277301.txt">Table of n, a(n) for n = 1..300</a>
%F A277301 G.f. A(x) also satisfies:
%F A277301 (1) A(x) = x + 5 * A( 3*x/5 + 2*A(x)/5 )^2.
%F A277301 (2) A(x) = -3*x/2 + 5/2 * Series_Reversion(x - 2*A(x)^2).
%F A277301 (3) R(x) = -2*x/3 + 5/3 * Series_Reversion(x + 3*A(x)^2), where R(A(x)) = x.
%F A277301 (4) R( sqrt( x/5 - R(x)/5 ) ) = 2*x/5 + 3*R(x)/5, where R(A(x)) = x.
%F A277301 a(n) = Sum_{k=0..n-1} A277295(n,k) * 2^k * 5^(n-k-1).
%e A277301 G.f.: A(x) = x + 5*x^2 + 70*x^3 + 1425*x^4 + 35410*x^5 + 999210*x^6 + 30855820*x^7 + 1020407105*x^8 + 35642665050*x^9 + 1302725802510*x^10 +...
%o A277301 (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 - 2*F^2) - 3*F^2, #A) ); A[n]}
%o A277301 for(n=1, 30, print1(a(n), ", "))
%Y A277301 Cf. A277295, A213591, A275765, A276360, A276361, A276362, A276363.
%Y A277301 Cf. A277300, A277302, A277303, A277304, A277305, A277306, A277307, A277308, A277309.
%Y A277301 Cf. A276364.
%K A277301 nonn
%O A277301 1,2
%A A277301 _Paul D. Hanna_, Oct 09 2016