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 A387017 #18 Aug 18 2025 23:01:18
%S A387017 1,6,28,139,660,3192,15260,73254,350848,1681650,8056608,38604748,
%T A387017 184963130,886226880,4246152960,20344613659,97476826932,467039887908,
%U A387017 2237722185188,10721572793580,51370139753240,246129134364792,1179275522335680,5650248517615128
%N A387017 Expansion of (Product_{k>=1} (1 - x^k)^2/(1 - 5*x^k + x^(2*k)) - 1)/3.
%C A387017 a(n) is the value at q = (5 + sqrt(21))/2 of C_n(q)/(q^{n-1}(q - 1)^2), where C_n(q) is the number of codimension n ideals of the algebra of two-variable Laurent polynomials over a finite field of order q. The number C_n(q) is a palindromic polynomial of degree 2n with integer coefficients in the variable q and it is divisible by (q-1)^2.
%H A387017 Christian Kassel and Christophe Reutenauer, <a href="http://arxiv.org/abs/1505.07229">Counting the ideals of given codimension of the algebra of Laurent polynomials in two variables</a>, arXiv:1505.07229 [math.AG], 2015-2016; Michigan Math. J. 67 (2018), 715-741.
%H A387017 Christian Kassel and Christophe Reutenauer, <a href="http://arxiv.org/abs/1610.07793">Complete determination of the zeta function of the Hilbert scheme of n points on a two-dimensional torus</a>, arXiv:1610.07793 [math.NT], 2016; The Ramanujan Journal 46 (2018), 633-655.
%H A387017 Christian Kassel and Christophe Reutenauer, <a href="http://arxiv.org/abs/2507.15780">Pairs of intertwined integer sequences</a>, arXiv:2507.15780 [math.NT], 2025.
%F A387017 G.f.: (Product_{k>=1} (1 - x^k)^2/(1 - 5*x^k + x^(2*k)) - 1)/3
%F A387017 a(2^k) = A030221(2^k-1). (Follows from Cor. 4.5 of Kassel and Reutenauer (2025).)
%F A387017 a(n) ~ (3 + sqrt(21))^(2*n-1) / (2^(2*n-1) * 3^n). - _Vaclav Kotesovec_, Aug 14 2025
%t A387017 nmax = 25; Rest[CoefficientList[Series[(Product[(1 - x^k)^2/(1 - 5*x^k + x^(2*k)), {k, 1, nmax}] - 1)/3, {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 14 2025 *)
%Y A387017 Cf. A030221, A386706, A329156.
%K A387017 nonn
%O A387017 1,2
%A A387017 _Christian Kassel_, Aug 13 2025