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 A274985 #25 Feb 16 2025 08:33:36
%S A274985 0,0,1,6,58,948,25992,1179016,87713040,10646068080,2101395344400,
%T A274985 673242645670320,349671381118477440,294206779308703578240,
%U A274985 400822226102433353285760,883965927408694948620295680,3155212287401150653204012531200
%N A274985 a(n) = ([n]_phi! - [n]_{1-phi}!)/sqrt(5), where [n]_q! is the q-factorial, phi = (1+sqrt(5))/2.
%H A274985 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-Factorial.html">q-Factorial</a>, <a href="https://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>.
%F A274985 [n]_phi! = (A274983(n) + a(n)*sqrt(5))/2.
%F A274985 [n]_{1-phi}! = (A274983(n) - a(n)*sqrt(5))/2.
%F A274985 a(n) ~ c * phi^(n*(n+3)/2) / sqrt(5), where c = QPochhammer(phi-1) = A276987 = 0.1208019218617061294237231569887920563043992516794... . - _Vaclav Kotesovec_, Sep 24 2016
%e A274985 For n = 3, [3]_phi! = 1060 + 474*sqrt(5), so A274983(5) = 2*1060 = 2120 and a(5) = 2*474 = 948.
%t A274985 Round@Table[(QFactorial[n, GoldenRatio] - QFactorial[n, 1 - GoldenRatio])/Sqrt[5], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
%Y A274985 Cf. A274983, A005329, A275706, A276474, A276688, A276987.
%K A274985 nonn
%O A274985 0,4
%A A274985 _Vladimir Reshetnikov_, Sep 23 2016