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 A383936 #19 Aug 28 2025 17:25:42
%S A383936 1,0,9,18,162,648,4050,20412,117369,639576,3628233,20360970,115858512,
%T A383936 659144304,3772679976,21637128240,124518397770,718139766240,
%U A383936 4151542099770,24045292507860,139520453553468,810834881716080,4719151317787452,27502373918849544
%N A383936 Expansion of 1 / ( (1-6*x) * (1+3*x)^2 )^(1/3).
%H A383936 Vincenzo Librandi, <a href="/A383936/b383936.txt">Table of n, a(n) for n = 0..1000</a>
%F A383936 a(n) = (-3)^n * Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(-1/3,k) * binomial(-2/3,n-k).
%F A383936 a(n) ~ 2^(n + 2/3) * 3^(n - 2/3) / (Gamma(1/3) * n^(2/3)). - _Vaclav Kotesovec_, Aug 18 2025
%F A383936 D-finite with recurrence n*a(n) +3*(-n+1)*a(n-1) +18*(-n+1)*a(n-2)=0. - _R. J. Mathar_, Aug 26 2025
%t A383936 CoefficientList[Series[1/((1-6*x)*(1+3*x)^2)^(1/3),{x,0,33}],x] (* _Vincenzo Librandi_, Aug 28 2025 *)
%o A383936 (PARI) a(n) = (-3)^n*sum(k=0, n, 2^k*(-1)^(n-k)*binomial(-1/3, k)*binomial(-2/3, n-k));
%o A383936 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1 / ( (1-6*x) * (1+3*x)^2 )^(1/3); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 28 2025
%Y A383936 Cf. A383935.
%K A383936 nonn,easy,changed
%O A383936 0,3
%A A383936 _Seiichi Manyama_, Aug 18 2025