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 A383754 #18 May 10 2025 11:28:06
%S A383754 1,65,2743,96005,3041143,90873965,2619766591,73828050725,
%T A383754 2050312110055,56398823205725,1541678963379919,41967937119356885,
%U A383754 1139327805030810487,30873653666483535245,835604944706085813727,22597672980558843070085,610791835087816964370439
%N A383754 Expansion of 1/Product_{k=0..3} (1 - 2^k * 3^(3-k) * x).
%H A383754 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (65,-1482,14040,-46656).
%F A383754 a(n) = A383753(n+3,3).
%F A383754 a(n) = 2^(3*n) * q-binomial(n+3, 3, 3/2).
%F A383754 G.f.: exp( Sum_{k>=1} f(4*k)/f(k) * x^k/k ), where f(k) = 3^k - 2^k.
%F A383754 a(n) = (-8^(n+2) + 38*12^(n+1) - 57*18^(n+1) + 27^(n+2))/95.
%F A383754 a(n) = 65*a(n-1) - 1482*a(n-2) + 14040*a(n-3) - 46656*a(n-4).
%o A383754 (PARI) a(n) = (-8^(n+2)+38*12^(n+1)-57*18^(n+1)+27^(n+2))/95;
%o A383754 (Sage)
%o A383754 def a(n): return 2^(3*n)*q_binomial(n+3, 3, 3/2)
%Y A383754 Cf. A006101, A383753.
%K A383754 nonn,easy
%O A383754 0,2
%A A383754 _Seiichi Manyama_, May 09 2025