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 A247850 #25 Feb 16 2025 08:33:23
%S A247850 0,-8,-16,3816,23008,80600,214992,483784,967616,1774008,3041200,
%T A247850 4941992,7687584,11531416,16773008,23761800,32900992,44651384,
%U A247850 59535216,78140008,101122400,129211992,163215184,204019016,252595008,310003000,377394992,456018984
%N A247850 The 5th Hermite Polynomial evaluated at n: H_5(n) = 32*n^5 - 160*n^3 + 120*n.
%H A247850 Vincenzo Librandi, <a href="/A247850/b247850.txt">Table of n, a(n) for n = 0..1000</a>
%H A247850 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HermitePolynomial.html">Hermite Polynomial</a>.
%H A247850 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A247850 G.f.: -x*(8-32*x-3792*x^2-32*x^3+8*x^4)/(x-1)^6.
%F A247850 a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).
%t A247850 Table[32 n^5 - 160 n^3 + 120 n, {n, 0, 30}]
%o A247850 (PARI) a(n)=32*n^5-160*n^3+120*n \\ _Charles R Greathouse IV_, Oct 07 2015
%o A247850 (Python)
%o A247850 from sympy import hermite
%o A247850 def A247850(n): return hermite(5,n) # _Chai Wah Wu_, Jan 06 2022
%Y A247850 Cf. Hermite_k(n): A005843 (k=1), A060626 (k=2), A163322 (k=3), A163323 (k=4), this sequence (k=5), A247851 (k=6), A247852 (k=7), A247853 (k=8), A247854 (k=9), A247855 (k=10).
%K A247850 sign,easy
%O A247850 0,2
%A A247850 _Vincenzo Librandi_, Sep 25 2014