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 A383757 #13 May 09 2025 16:19:57
%S A383757 1,175,19525,1776775,144142141,10884484975,783802527925,
%T A383757 54630820881175,3721247723926381,249337226367003775,
%U A383757 16508103305566548325,1083453420457687217575,70652392978007927384221,4585369275138131990546575,296541443098920894741800725,19127262646595562017053105975
%N A383757 Expansion of 1/Product_{k=0..3} (1 - 3^k * 4^(3-k) * x).
%H A383757 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (175,-11100,302400,-2985984).
%F A383757 a(n) = A383755(n+3,3).
%F A383757 a(n) = 3^(3*n) * q-binomial(n+3, 3, 4/3).
%F A383757 G.f.: exp( Sum_{k>=1} f(4*k)/f(k) * x^k/k ), where f(k) = 4^k - 3^k.
%F A383757 a(n) = (-27^(n+2) + 111*36^(n+1) - 148*48^(n+1) + 64^(n+2))/259.
%F A383757 a(n) = 175*a(n-1) - 11100*a(n-2) + 302400*a(n-3) - 2985984*a(n-4).
%o A383757 (PARI) a(n) = (-27^(n+2)+111*36^(n+1)-148*48^(n+1)+64^(n+2))/259;
%o A383757 (Sage)
%o A383757 def a(n): return 3^(3*n)*q_binomial(n+3, 3, 4/3)
%Y A383757 Cf. A383755.
%K A383757 nonn,easy
%O A383757 0,2
%A A383757 _Seiichi Manyama_, May 09 2025