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 A062189 #26 Apr 18 2025 17:44:38
%S A062189 0,2,20,126,648,2970,12636,51030,198288,747954,2755620,9959598,
%T A062189 35429400,124357194,431530092,1482720390,5050815264,17075199330,
%U A062189 57338232372,191385721566,635369601960,2099044209402,6903833113980
%N A062189 a(n) = 2 * 3^(n-2)*n*(1+2*n).
%C A062189 Define a triangle with left (first) column T(n,0)=n^2 for n=0,1,2,3.. and the remaining terms T(r,c) = T(r-1,c-1) + 2*T(r,c-1). Then T(n,n) = a(n) on the diagonal. T(n,1) = A056105(n). - _J. M. Bergot_, Jan 26 2013
%H A062189 Harry J. Smith, <a href="/A062189/b062189.txt">Table of n, a(n) for n = 0..200</a>
%H A062189 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-27,27).
%F A062189 a(n) = A002943(n)*A000244(n-2). Binomial transform of A007758.
%F A062189 G.f.: 2*x*(1+x)/(1-3*x)^3. - _Ralf Stephan_, Mar 13 2003
%F A062189 a(n) = 2*A077616(n). - _R. J. Mathar_, Jan 29 2013
%F A062189 E.g.f.: 2*x*(1+2*x)*exp(3*x). - _G. C. Greubel_, Jun 06 2019
%t A062189 Table[2*3^(n-2)*n*(1+2*n), {n,0,30}] (* _G. C. Greubel_, Jun 06 2019 *)
%t A062189 LinearRecurrence[{9,-27,27},{0,2,20},30] (* _Harvey P. Dale_, Jun 08 2022 *)
%o A062189 (PARI) { for (n=0, 200, write("b062189.txt", n, " ", n*(4*n + 2)*3^(n - 2)) ) } \\ _Harry J. Smith_, Aug 02 2009
%o A062189 (Magma) [2*3^(n-2)*n*(1+2*n): n in [0..30]]; // _G. C. Greubel_, Jun 06 2019
%o A062189 (Sage) [2*3^(n-2)*n*(1+2*n) for n in (0..30)] # _G. C. Greubel_, Jun 06 2019
%o A062189 (GAP) List([0..30], n-> 2*3^(n-2)*n*(1+2*n)); # _G. C. Greubel_, Jun 06 2019
%K A062189 nonn,easy
%O A062189 0,2
%A A062189 _Henry Bottomley_, Jun 13 2001