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 A361779 #27 May 11 2023 14:23:25
%S A361779 1,1,2,5,10,21,51,121,282,688,1704,4212,10528,26626,67630,172590,
%T A361779 443156,1143034,2958829,7687875,20043717,52410511,137417383,361225349,
%U A361779 951755240,2513057208,6648904064,17624116631,46796906873,124460500129,331517863145,884305712723,2362007410465
%N A361779 Expansion of g.f. A(x) satisfying 1/x = Sum_{n=-oo..+oo} x^n * (x^(2*n) - (-1)^n*A(x))^(n+1).
%H A361779 Paul D. Hanna, <a href="/A361779/b361779.txt">Table of n, a(n) for n = 0..400</a>
%F A361779 G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.
%F A361779 (1) 1/x = Sum_{n=-oo..+oo} x^n * ((-x^2)^n - A(x))^(n+1).
%F A361779 (2) 1 = Sum_{n=-oo..+oo} x^(n*(2*n+1)) / (1 - A(x)*(-x^2)^(n+1))^n.
%F A361779 a(n) ~ c * d^n / n^(3/2), where d = 2.791690127253271... and c = 2.581668816660... - _Vaclav Kotesovec_, May 11 2023
%e A361779 G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 10*x^4 + 21*x^5 + 51*x^6 + 121*x^7 + 282*x^8 + 688*x^9 + 1704*x^10 + 4212*x^11 + 10528*x^12 + ...
%e A361779 SPECIFIC VALUES.
%e A361779 A(1/4) = 1.54381930928063102950885404708273996504264975892127868985...
%e A361779 A(3/10) = 1.8845579890166759655973763714847523770459496427989251...
%e A361779 A(1/3) = 2.35223102094304184442834405817178151095013948472323960819...
%o A361779 (PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
%o A361779 A[#A] = polcoeff( sum(m=-#A, #A, x^m * (x^(2*m) - (-1)^m*Ser(A))^(m+1) ), #A-1) ); A[n+1]}
%o A361779 for(n=0, 30, print1(a(n), ", "))
%Y A361779 Cf. A361778.
%K A361779 nonn
%O A361779 0,3
%A A361779 _Paul D. Hanna_, May 10 2023