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 A383937 #19 Aug 28 2025 12:33:25
%S A383937 1,6,33,180,990,5508,30978,175824,1005345,5782590,33418737,193876092,
%T A383937 1128297276,6583492080,38498441400,225550220544,1323563204394,
%U A383937 7777806812892,45762197971050,269545947941160,1589219394582996,9378142402189176,55385341859409948
%N A383937 Expansion of 1 / ( (1-3*x) * (1-6*x) )^(2/3).
%H A383937 Vincenzo Librandi, <a href="/A383937/b383937.txt">Table of n, a(n) for n = 0..1000</a>
%F A383937 G.f.: B(x)^(2/3), where B(x) is the g.f. of A016137.
%F A383937 a(n) = (-3)^n * Sum_{k=0..n} 2^k * binomial(-2/3,k) * binomial(-2/3,n-k).
%F A383937 a(n) ~ Gamma(1/3) * 2^(n - 1/3) * 3^(n + 1/2) / (Pi * n^(1/3)). - _Vaclav Kotesovec_, Aug 18 2025
%F A383937 D-finite with recurrence n*a(n) +3*(-3*n+1)*a(n-1) +6*(3*n-2)*a(n-2)=0. - _R. J. Mathar_, Aug 26 2025
%t A383937 CoefficientList[Series[1/((1-3*x)*(1-6*x))^(2/3),{x,0,33}],x] (* _Vincenzo Librandi_, Aug 28 2025 *)
%o A383937 (PARI) a(n) = (-3)^n*sum(k=0, n, 2^k*binomial(-2/3, k)*binomial(-2/3, n-k));
%o A383937 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1 / ( (1-3*x) * (1-6*x) )^(2/3); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 28 2025
%Y A383937 Cf. A016137, A383935.
%K A383937 nonn,easy,changed
%O A383937 0,2
%A A383937 _Seiichi Manyama_, Aug 18 2025