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 A307413 #13 Aug 29 2019 21:56:06
%S A307413 1,1,2,7,26,102,420,1787,7794,34666,156636,716982,3317700,15494156,
%T A307413 72935624,345701843,1648489762,7902956738,38067806892,184152092450,
%U A307413 894259126540,4357738501844,21302682030328,104439435098718,513390992000340,2529846489669412,12494572784556440
%N A307413 G.f. A(x) satisfies: A(x) = 1 + x*A(x)/(1 - x*A(x) - 2*x^2*A(x)^2).
%C A307413 Unsigned version of A326564. - _Paul D. Hanna_, Aug 28 2019
%F A307413 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} Jacobsthal(k)*x^k*A(x)^k, where Jacobsthal = A001045.
%F A307413 G.f.: A(x) = (1/x)*Series_Reversion(x*(1 + x)*(1 - 2*x)/(1 - 2*x^2)).
%F A307413 From _Paul D. Hanna_, Aug 29 2019: (Start)
%F A307413 G.f. A(x) satisfies: 0 = Sum_{n>=1} (1-(-1)^n - 2*A(x))^n * x^n / n.
%F A307413 G.f. A(x) satisfies: log(1 - 4*x^2*A(x)^2)/2 = arctanh(2*x - 2*x*A(x)). (End)
%t A307413 terms = 26; A[_] = 0; Do[A[x_] = 1 + x A[x]/(1 - x A[x] - 2 x^2 A[x]^2) + O[x]^(terms + 1) // Normal, {terms + 1}]; CoefficientList[A[x], x]
%t A307413 terms = 27; A[_] = 0; Do[A[x_] = 1 + Sum[(1/3) (2^k - (-1)^k) x^k A[x]^k, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%t A307413 terms = 27; CoefficientList[1/x InverseSeries[Series[x (1 + x) (1 - 2 x)/(1 - 2 x^2), {x, 0, terms}], x], x]
%Y A307413 Cf. A001045, A049124, A307411, A307412.
%Y A307413 Cf. A326564.
%K A307413 nonn
%O A307413 0,3
%A A307413 _Ilya Gutkovskiy_, Apr 07 2019