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 A213628 #7 Dec 16 2024 14:27:37
%S A213628 1,1,3,14,85,616,5072,46013,450739,4702265,51731956,595874703,
%T A213628 7147366614,88905147730,1143097097833,15152617826426,206646826047563,
%U A213628 2894398418226395,41577147999077079,611779190051375147,9211548488261257610,141802624561414800815
%N A213628 G.f. satisfies: A(x) = 1 - (x^2/A(x)) / A( x^2/A(x) ).
%F A213628 G.f.: A(x) = x^2/(x - G(x)^2) where G(x) is the g.f. of A213591 such that G(x^2/A(x)) = G(x - G(x)^2) = x.
%F A213628 G.f.: A(x) = Series_Reversion(x*F(x)) where F(x) = 1 + x*F(1 - 1/F(x))^2 is the g.f. of A212411.
%e A213628 G.f.: A(x) = x + x^2 + 3*x^3 + 14*x^4 + 85*x^5 + 616*x^6 + 5072*x^7 +...
%e A213628 Related expansions:
%e A213628 x^2/A(x) = x - x^2 - 2*x^3 - 9*x^4 - 56*x^5 - 420*x^6 - 3572*x^7 -...
%e A213628 A(x^2/A(x)) = x - x^3 - 7*x^4 - 50*x^5 - 395*x^6 - 3436*x^7 -...
%e A213628 A(x) = x^2/Series_Reversion(G(x)) where G(x) is the g.f. of A213591:
%e A213628 G(x) = x + x^2 + 4*x^3 + 24*x^4 + 178*x^5 + 1512*x^6 + 14152*x^7 +...
%e A213628 such that G(x - G(x)^2) = x.
%o A213628 (PARI) {a(n)=local(A=x,G=x); if(n<1, 0, for(i=1, n, G=serreverse(x - G^2+x*O(x^n)));A=x^2/(x-G^2);polcoeff(A, n))}
%o A213628 for(n=1,25,print1(a(n),", "))
%Y A213628 Cf. A213591, A212411.
%K A213628 nonn
%O A213628 1,3
%A A213628 _Paul D. Hanna_, Jun 16 2012