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 A317403 a(n)=(-1)^((n-2)*(n-1)/2)*2^(n-1)*n^(n-3). 1
 1, 1, -4, -32, 400, 6912, -153664, -4194304, 136048896, 5120000000, -219503494144, -10567230160896, 564668382613504, 33174037869887488, -2125764000000000000, -147573952589676412928, 11034809241396899282944, 884295678882933431599104, -75613185918270483380568064 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Discriminant of Fibonacci polynomials. Fibonacci polynomials are defined as F(0)=0, F(1)=1 and F(n)=x*F(n-1)+F(n-2) for n>1. Coefficients are given in triangle A168561 with offset 1. LINKS Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018. Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles, 2018. R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14. R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2. Eric Weisstein's World of Mathematics, Discriminant Eric Weisstein's World of Mathematics, Fibonacci Polynomial MATHEMATICA Array[(-1)^((#-2)*(#-1)/2)*2^(#-1)*#^(#-3)&, 20] PROG (PARI) concat([1], [poldisc(p) | p<-Vec(x/(1-x^2-y*x) - x + O(x^20))]) \\ Andrew Howroyd, Aug 26 2018 (MAGMA) [(-1)^((n-2)*(n-1) div 2)*2^(n-1)*n^(n-3): n in [1..20]]; // Vincenzo Librandi, Aug 27 2018 CROSSREFS Cf. A006645, A001629, A001871, A006645, A007701, A045618, A045925, A093967, A168561, A193678, A317404, A317405, A317408, A317451, A318184, A318197. Essentially the same as A127670. Sequence in context: A113131 A195762 A127670 * A243468 A317677 A191459 Adjacent sequences:  A317400 A317401 A317402 * A317404 A317405 A317406 KEYWORD sign AUTHOR Rigoberto Florez, Aug 26 2018 STATUS approved

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Last modified May 12 19:15 EDT 2021. Contains 343829 sequences. (Running on oeis4.)