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 A033594 #39 Sep 08 2022 08:44:51
%S A033594 -1,0,15,80,231,504,935,1560,2415,3536,4959,6720,8855,11400,14391,
%T A033594 17864,21855,26400,31535,37296,43719,50840,58695,67320,76751,87024,
%U A033594 98175,110240,123255,137256,152279,168360
%N A033594 a(n) = (n-1)*(2*n-1)*(3*n-1).
%C A033594 The sequence of n such that n is prime and (2*n+1) is prime is the sequence of Sophie Germain primes A005384 and the subsequence of those for which in addition (3*n+2) is prime is A067256. - _Jonathan Vos Post_, Dec 15 2004
%H A033594 Vincenzo Librandi, <a href="/A033594/b033594.txt">Table of n, a(n) for n = 0..1000</a>
%H A033594 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A033594 a(n)*A016921(n) + 1 = A051866(n)^2. - _Bruno Berselli_, May 23 2011
%F A033594 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), with a(0)=-1, a(1)=0, a(2)=15, a(3)=80. - _Harvey P. Dale_, Aug 23 2012
%F A033594 G.f.: (-1 +4*x +9*x^2 +24*x^3)/(1-x)^4. - _R. J. Mathar_, Feb 06 2017
%F A033594 E.g.f.: (-1 + x + 7*x^2 + 6*x^3)*exp(x). - _G. C. Greubel_, Mar 05 2020
%F A033594 From _Amiram Eldar_, Jan 03 2021: (Start)
%F A033594 Sum_{n>=2} 1/a(n) = (7 - sqrt(3)*Pi - 16*log(2) + 9*log(3))/4.
%F A033594 Sum_{n>=2} (-1)^n/a(n) = Pi - 7/4 - sqrt(3)*Pi/2 + 2*log(2). (End)
%p A033594 A033594:=n->(n-1)*(2*n-1)*(3*n-1); seq(A033594(n), n=0..40); # _Wesley Ivan Hurt_, Feb 24 2014
%t A033594 Table[(n-1)*(2*n-1)*(3*n-1),{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2010 *)
%t A033594 LinearRecurrence[{4,-6,4,-1},{-1,0,15,80},40] (* _Harvey P. Dale_, Aug 23 2012 *)
%o A033594 (Magma) [(n-1)*(2*n-1)*(3*n-1): n in [0..40]]; // _Vincenzo Librandi_, May 24 2011
%o A033594 (PARI) vector(41, n, my(m=n-1); (m-1)*(2*m-1)*(3*m-1) ) \\ _G. C. Greubel_, Mar 05 2020
%o A033594 (Sage) [-1]+[n^3*rising_factorial((n-1)/n, 3) for n in (1..40)] # _G. C. Greubel_, Mar 05 2020
%o A033594 (GAP) List([0..40], n-> (n-1)*(2*n-1)*(3*n-1) ); # _G. C. Greubel_, Mar 05 2020
%Y A033594 Cf. A005384, A016921, A067256.
%K A033594 sign,easy
%O A033594 0,3
%A A033594 _N. J. A. Sloane_