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 A274983 #29 Feb 16 2025 08:33:36
%S A274983 2,2,3,14,130,2120,58120,2636360,196132320,23805331920,4698862837680,
%T A274983 1505416321070640,781888977967152000,657866357975539785600,
%U A274983 896265744457831561756800,1976607903479486428467148800,7055269158071576119808840371200
%N A274983 a(n) = [n]_phi! + [n]_{1-phi}!, where [n]_q! is the q-factorial, phi = (1+sqrt(5))/2.
%H A274983 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 A274983 a(n) ~ c * phi^(n*(n+3)/2), where c = QPochhammer(phi-1) = A276987 = 0.1208019218617061294237231569887920563043992516794... . - _Vaclav Kotesovec_, Sep 24 2016
%F A274983 From _Vladimir Reshetnikov_, Sep 24 2016 (Start)
%F A274983 [n]_phi! = (a(n) + A274985(n)*sqrt(5))/2.
%F A274983 [n]_{1-phi}! = (a(n) - A274985(n)*sqrt(5))/2. (End)
%e A274983 For n = 3, [3]_phi! = 1060 + 474*sqrt(5), so a(5) = 2*1060 = 2120 and A274985(5) = 2*474 = 948.
%t A274983 Round@Table[QFactorial[n, GoldenRatio] + QFactorial[n, 1 - GoldenRatio], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
%Y A274983 Cf. A274985, A005329, A275706, A276474, A276688, A276987.
%K A274983 nonn
%O A274983 0,1
%A A274983 _Vladimir Reshetnikov_, Sep 23 2016