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 A385117 #26 Sep 02 2025 04:07:50 %S A385117 1,9,54,243,810,1701,0,-16038,-56862,0,817938,3241134,0,-53872371, %T A385117 -224386200,0,4017339666,17216031195,0,-322568743770,-1408090130370,0, %U A385117 27206369474544,120309415164990,0,-2376712950727284,-10611290417552118,0,213172869272924088 %N A385117 G.f. A(x) satisfies A(x) = 1 + 9*x*A(x)^(2/3). %H A385117 Paolo Xausa, <a href="/A385117/b385117.txt">Table of n, a(n) for n = 0..1000</a> %F A385117 a(n) = 9^n * binomial(2*n/3+1,n)/(2*n/3+1). %F A385117 G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^(1/3)). %F A385117 G.f.: 1/B(-x), where B(x) is the g.f. of A135864. %F A385117 G.f.: B(x)^3, where B(x) is the g.f. of A376636. %F A385117 a(3*n) = 0 for n > 1. %F A385117 D-finite with recurrence (n-1)*(n-2)*a(n) + 54*(2*n-3)*(n-6)*a(n-3) = 0. - _R. J. Mathar_, Jul 30 2025 %F A385117 a(n) ~ A128834(n) * 2^(2*n/3) * 3^(n+3/2) / (sqrt(Pi) * n^(3/2)). - _Amiram Eldar_, Sep 02 2025 %t A385117 A385117[n_] := 9^n*Binomial[2*n/3 + 1, n]/(2*n/3 + 1); %t A385117 Array[A385117, 35, 0] (* _Paolo Xausa_, Aug 01 2025 *) %o A385117 (PARI) a(n) = 9^n*binomial(2*n/3+1, n)/(2*n/3+1); %Y A385117 Cf. A135864, A214668, A385119. %Y A385117 Cf. A376636. %K A385117 sign,changed %O A385117 0,2 %A A385117 _Seiichi Manyama_, Jun 18 2025