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 A380274 #11 Feb 16 2025 08:34:07
%S A380274 1,1,2,18,522,34986,4524240,1003172616,351349509504,182985164256000,
%T A380274 135303274820730372,136936922140937021688,184146557651652262521738,
%U A380274 321051865325352021467189658,710866983641078174204266934736,1964068265459581480020247325821224
%N A380274 Sum of cubes of coefficients of q in the q-factorials.
%H A380274 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-Factorial.html">q-Factorial</a>.
%F A380274 a(n) = Sum_{k>=0} A008302(n,k)^3.
%F A380274 Conjecture: a(n) ~ 6*sqrt(3) * n!^3 / (Pi * n^3).
%e A380274 a(4) = 1^3 + 3^3 + 5^3 + 6^3 + 5^3 + 3^3 + 1^3 = 522.
%t A380274 Table[Total[CoefficientList[Expand[Product[Sum[x^i, {i, 0, m}], {m, 1, n-1}]], x]^3], {n, 0, 15}]
%o A380274 (PARI) a(n) = my(v=Vec(prod(k=1, n, (1-q^k)/(1-q)))); sum(i=1, #v, v[i]^3); \\ _Michel Marcus_, Jan 18 2025
%Y A380274 Cf. A008302, A127728, A380275.
%K A380274 nonn
%O A380274 0,3
%A A380274 _Vaclav Kotesovec_, Jan 18 2025