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A163322 The 3rd Hermite Polynomial evaluated at n: H_3(n) = 8*n^3 - 12*n. 3

%I

%S 0,-4,40,180,464,940,1656,2660,4000,5724,7880,10516,13680,17420,21784,

%T 26820,32576,39100,46440,54644,63760,73836,84920,97060,110304,124700,

%U 140296,157140,175280,194764,215640,237956,261760,287100,314024,342580

%N The 3rd Hermite Polynomial evaluated at n: H_3(n) = 8*n^3 - 12*n.

%H Vincenzo Librandi, <a href="/A163322/b163322.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/He#Hermite">Index entries for sequences related to Hermite polynomials</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HermitePolynomial.html">Hermite Polynomial</a>.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = 8*n^3 - 12*n.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

%F G.f.: -4*x*(1-14*x+x^2)/(x-1)^4.

%p A163322 := proc(n) orthopoly[H](3,n) ; end: seq(A163322(n),n=0..80) ; # _R. J. Mathar_, Jul 26 2009

%t CoefficientList[Series[-4*x*(1-14*x+x^2)/(x-1)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Mar 05 2012 *)

%t LinearRecurrence[{4,-6,4,-1},{0,-4,40,180},40] (* _Harvey P. Dale_, Aug 14 2014 *)

%o (MAGMA) [8*n^3-12*n: n in [0..40]]; // _Vincenzo Librandi_, Mar 05 2012

%o (PARI) a(n)=8*n^3-12*n \\ _Charles R Greathouse IV_, Jan 29 2016

%Y Cf. A060821, A059343.

%K sign,easy

%O 0,2

%A _Vincenzo Librandi_, Jul 25 2009

%E Edited by _R. J. Mathar_, Jul 26 2009

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Last modified August 19 04:59 EDT 2019. Contains 326109 sequences. (Running on oeis4.)