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 A163322 The 3rd Hermite Polynomial evaluated at n: H_3(n) = 8*n^3 - 12*n. 3
 0, -4, 40, 180, 464, 940, 1656, 2660, 4000, 5724, 7880, 10516, 13680, 17420, 21784, 26820, 32576, 39100, 46440, 54644, 63760, 73836, 84920, 97060, 110304, 124700, 140296, 157140, 175280, 194764, 215640, 237956, 261760, 287100, 314024, 342580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Hermite Polynomial. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 8*n^3 - 12*n. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). G.f.: -4*x*(1-14*x+x^2)/(x-1)^4. MAPLE A163322 := proc(n) orthopoly[H](3, n) ; end: seq(A163322(n), n=0..80) ; # R. J. Mathar, Jul 26 2009 MATHEMATICA CoefficientList[Series[-4*x*(1-14*x+x^2)/(x-1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 05 2012 *) LinearRecurrence[{4, -6, 4, -1}, {0, -4, 40, 180}, 40] (* Harvey P. Dale, Aug 14 2014 *) PROG (MAGMA) [8*n^3-12*n: n in [0..40]]; // Vincenzo Librandi, Mar 05 2012 (PARI) a(n)=8*n^3-12*n \\ Charles R Greathouse IV, Jan 29 2016 CROSSREFS Cf. A060821, A059343. Sequence in context: A248964 A224086 A271013 * A238328 A009355 A061132 Adjacent sequences:  A163319 A163320 A163321 * A163323 A163324 A163325 KEYWORD sign,easy AUTHOR Vincenzo Librandi, Jul 25 2009 EXTENSIONS Edited by R. J. Mathar, Jul 26 2009 STATUS approved

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Last modified July 22 02:26 EDT 2019. Contains 325210 sequences. (Running on oeis4.)