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 A383756 #13 May 09 2025 11:41:36
%S A383756 1,37,925,19525,375661,6828757,119609725,2042733925,34274529421,
%T A383756 567869330677,9323118394525,152047784616325,2467581667044781,
%U A383756 39901653896747797,643493505828795325,10356906506162786725,166444482073618177741,2671936126059753592117
%N A383756 Expansion of 1/Product_{k=0..2} (1 - 3^k * 4^(2-k) * x).
%H A383756 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (37,-444,1728).
%F A383756 a(n) = A383755(n+2,2).
%F A383756 a(n) = 3^(2*n) * q-binomial(n+2, 2, 4/3).
%F A383756 G.f.: exp( Sum_{k>=1} f(3*k)/f(k) * x^k/k ), where f(k) = 4^k - 3^k.
%F A383756 a(n) = (3*9^(n+1) - 7*12^(n+1) + 4*16^(n+1))/7.
%F A383756 a(n) = 37*a(n-1) - 444*a(n-2) + 1728*a(n-3).
%o A383756 (PARI) a(n) = (3*9^(n+1)-7*12^(n+1)+4*16^(n+1))/7;
%o A383756 (Sage)
%o A383756 def a(n): return 3^(2*n)*q_binomial(n+2, 2, 4/3)
%Y A383756 Cf. A383755.
%K A383756 nonn,easy
%O A383756 0,2
%A A383756 _Seiichi Manyama_, May 09 2025