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 A386006 #28 Aug 27 2025 05:18:39
%S A386006 1,2,11,64,386,2380,14893,94184,600370,3850756,24821333,160645504,
%T A386006 1043243132,6794414896,44360053772,290244832992,1902631226010,
%U A386006 12493030680180,82153313341429,540953389469312,3566279609565226,23536562549993228,155489358646406149
%N A386006 a(n) = Sum_{k=0..n} binomial(3*n-2,k).
%H A386006 Vincenzo Librandi, <a href="/A386006/b386006.txt">Table of n, a(n) for n = 0..1000</a>
%F A386006 a(n) = [x^n] (1+x)^(3*n-2)/(1-x).
%F A386006 a(n) = [x^n] 1/((1-x)^(2*n-2) * (1-2*x)).
%F A386006 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(3*n-2,k) * binomial(3*n-k-3,n-k).
%F A386006 a(n) = Sum_{k=0..n} 2^k * binomial(3*n-k-3,n-k).
%F A386006 G.f.: 1/(g * (2-g) * (3-2*g)) where g = 1+x*g^3 is the g.f. of A001764.
%t A386006 Table[Sum[Binomial[3*n-2,k],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 27 2025 *)
%o A386006 (PARI) a(n) = sum(k=0, n, binomial(3*n-2, k));
%o A386006 (Magma) [&+[Binomial(3*n-2,k): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Aug 27 2025
%Y A386006 Cf. A066380, A160906, A385823, A387007, A387008, A387033.
%Y A386006 Cf. A001764, A047099, A165817.
%K A386006 nonn,changed
%O A386006 0,2
%A A386006 _Seiichi Manyama_, Aug 13 2025