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 A163322 #32 Feb 16 2025 08:33:11
%S A163322 0,-4,40,180,464,940,1656,2660,4000,5724,7880,10516,13680,17420,21784,
%T A163322 26820,32576,39100,46440,54644,63760,73836,84920,97060,110304,124700,
%U A163322 140296,157140,175280,194764,215640,237956,261760,287100,314024,342580
%N A163322 The 3rd Hermite Polynomial evaluated at n: H_3(n) = 8*n^3 - 12*n.
%H A163322 Vincenzo Librandi, <a href="/A163322/b163322.txt">Table of n, a(n) for n = 0..1000</a>
%H A163322 <a href="/index/He#Hermite">Index entries for sequences related to Hermite polynomials</a>
%H A163322 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HermitePolynomial.html">Hermite Polynomial</a>.
%H A163322 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A163322 a(n) = 8*n^3 - 12*n.
%F A163322 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A163322 G.f.: -4*x*(1-14*x+x^2)/(x-1)^4.
%p A163322 A163322 := proc(n) orthopoly[H](3,n) ; end: seq(A163322(n),n=0..80) ; # _R. J. Mathar_, Jul 26 2009
%t A163322 CoefficientList[Series[-4*x*(1-14*x+x^2)/(x-1)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Mar 05 2012 *)
%t A163322 LinearRecurrence[{4,-6,4,-1},{0,-4,40,180},40] (* _Harvey P. Dale_, Aug 14 2014 *)
%o A163322 (Magma) [8*n^3-12*n: n in [0..40]]; // _Vincenzo Librandi_, Mar 05 2012
%o A163322 (PARI) a(n)=8*n^3-12*n \\ _Charles R Greathouse IV_, Jan 29 2016
%o A163322 (Python)
%o A163322 from sympy import hermite
%o A163322 def A163322(n): return hermite(3,n) # _Chai Wah Wu_, Jan 06 2022
%Y A163322 Cf. A060821, A059343.
%K A163322 sign,easy
%O A163322 0,2
%A A163322 _Vincenzo Librandi_, Jul 25 2009
%E A163322 Edited by _R. J. Mathar_, Jul 26 2009