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 A377268 #20 Aug 05 2025 06:59:25 %S A377268 1,-3,0,9,27,0,-324,-1215,0,18711,75816,0,-1301265,-5484996,0, %T A377268 100048689,431943435,0,-8192222064,-35942240565,0,700434986472, %U A377268 3108770417700,0,-61805774132388,-276711654879477,0,5586291123504300,25180760594032407,0,-514555201693265040 %N A377268 G.f. satisfies A(x) = (1 - 9*x*A(x))^(1/3). %H A377268 Paolo Xausa, <a href="/A377268/b377268.txt">Table of n, a(n) for n = 0..1000</a> %H A377268 <a href="/index/Res#revert">Index entries for reversions of series</a> %F A377268 G.f.: (1/x) * Series_Reversion( x/(1-9*x)^(1/3) ). %F A377268 a(n) = 9^n * binomial(2*n/3 - 4/3,n)/(n+1). %F A377268 From _Seiichi Manyama_, Jun 19 2025: (Start) %F A377268 G.f. A(x) satisfies A(x) = 1/A(-x/A(x)). %F A377268 a(3*n+2) = 0 for n >= 0. (End) %t A377268 A377268[n_] := 9^n*Binomial[(2*n - 4)/3, n]/(n + 1); %t A377268 Array[A377268, 35, 0] (* _Paolo Xausa_, Aug 05 2025 *) %o A377268 (PARI) a(n) = 9^n*binomial(2*n/3-4/3, n)/(n+1); %Y A377268 Cf. A104624. %K A377268 sign,easy %O A377268 0,2 %A A377268 _Seiichi Manyama_, Oct 22 2024