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 A385119 #25 Sep 02 2025 04:07:57 %S A385119 1,9,135,2430,48195,1015740,22320522,505692720,11727186075, %T A385119 277005649635,6641224015140,161193712078854,3953072078945730, %U A385119 97801207953712200,2438092322304120720,61182608813245896840,1544295394480280288715,39180450803555268621540 %N A385119 G.f. A(x) satisfies A(x) = 1 + 9*x*A(x)^(5/3). %H A385119 Paolo Xausa, <a href="/A385119/b385119.txt">Table of n, a(n) for n = 0..650</a> %F A385119 a(n) = 9^n * binomial(5*n/3+1,n)/(5*n/3+1). %F A385119 G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^(7/3)). %F A385119 G.f.: B(x)^3, where B(x) is the g.f. of A245114. %F A385119 D-finite with recurrence 2*n*(n-1)*(n-2)*(2*n+3)*a(n) - 135*(5*n-9)*(5*n-3)*(5*n-12)*(5*n-6)*a(n-3) = 0. - _R. J. Mathar_, Jul 30 2025 %F A385119 a(n) ~ 3^(n+1) * 5^(5*n/3+1/2) / (sqrt(Pi) * 2^(2*(n+3)/3) * n^(3/2)). - _Amiram Eldar_, Sep 02 2025 %t A385119 A385119[n_] := 9^n*Binomial[#, n]/# & [5*n/3 + 1]; %t A385119 Array[A385119, 20, 0] (* _Paolo Xausa_, Aug 05 2025 *) %o A385119 (PARI) a(n) = 9^n*binomial(5*n/3+1, n)/(5*n/3+1); %Y A385119 Cf. A135864, A214668, A385117. %Y A385119 Cf. A245114. %K A385119 nonn,changed %O A385119 0,2 %A A385119 _Seiichi Manyama_, Jun 18 2025