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 A136264 Expansion of (1+x)^2*(x^2-6*x+1)/(x-1)^4. 3
 1, 0, -16, -64, -160, -320, -560, -896, -1344, -1920, -2640, -3520, -4576, -5824, -7280, -8960, -10880, -13056, -15504, -18240, -21280, -24640, -28336, -32384, -36800, -41600, -46800, -52416, -58464, -64960, -71920, -79360, -87296, -95744, -104720, -114240, -124320, -134976, -146224, -158080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Inverse z-transform of the magnetization polynomial for the Ising model. This polynomial is the eighth power of the spontaneous magnetization for a two-dimensional square lattice. REFERENCES Terrel L. Hill, Statistical Mechanics: Principles and Selected Applications, Dover, New York, 1956, page 331 LINKS M. R. Sepanski, On Divisibility of Convolutions of Central Binomial Coefficients, Electronic Journal of Combinatorics, 21 (1) 2014, #P1.32. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 8n(1-n^2)/3, n>0. [R. J. Mathar, Mar 09 2009] MATHEMATICA CoefficientList[Series[(1+x)^2(x^2-6x+1)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 0, -16, -64, -160}, 40] (* Harvey P. Dale, Mar 15 2020 *) PROG (PARI) Vec((1+x)^2*(x^2-6*x+1)/(x-1)^4 + O(x^100)) \\ Altug Alkan, Oct 26 2015 CROSSREFS Essentially the same as A102860. Cf. A115046. Sequence in context: A309573 A205064 A102860 * A266103 A100184 A304845 Adjacent sequences:  A136261 A136262 A136263 * A136265 A136266 A136267 KEYWORD sign,easy AUTHOR Roger L. Bagula, Apr 07 2008 STATUS approved

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Last modified January 19 13:17 EST 2021. Contains 340270 sequences. (Running on oeis4.)