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 A350384 #24 Dec 25 2023 18:24:44 %S A350384 1,-1728,2985984,-5159780352,8916100448256,-15407021574586368, %T A350384 26623333280885243904,-46005119909369701466112, %U A350384 79496847203390844133441536,-137370551967459378662586974208,237376313799769806328950291431424,-410186270246002225336426103593500672 %N A350384 a(n) = (-1728)^n. %H A350384 Caroline Nunn, <a href="https://scholar.rose-hulman.edu/rhumj/vol22/iss2/3">A Proof of a Generalization of Niven's Theorem Using Algebraic Number Theory</a>, Rose-Hulman Undergraduate Mathematics Journal: Vol. 22, Iss. 2, Article 3 (2021). %H A350384 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (-1728). %F A350384 From Caroline Nunn, p. 9: (Start) %F A350384 a(n) = (3 + sqrt(-3))^(6*n). %F A350384 a(n) = Sum_{k=0..3*n} (-1)^k*binomial(6*n, 2*k)*3^(6*n-k). (End) %F A350384 O.g.f.: 1/(1 + 1728*x). %F A350384 E.g.f.: exp(-1728*x). %F A350384 a(n) = -1728*a(n-1) for n > 0. %F A350384 a(n) = (-12)^(3*n). %F A350384 a(n) = (A000244(n)*A262710(n))^3. %t A350384 LinearRecurrence[{-1728},{1},12] %t A350384 NestList[-1728#&,1,20] (* _Harvey P. Dale_, Dec 25 2023 *) %Y A350384 Cf. A000244, A000578, A001021, A008585, A008588, A262710. %K A350384 sign,easy %O A350384 0,2 %A A350384 _Stefano Spezia_, Dec 28 2021