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A317450 a(n)=(-1)^((n-2)*(n-1)/2)*2^((n-1)^2)*n^(n-3). 0

%I #49 Sep 28 2018 21:52:36

%S 1,1,-16,-2048,1638400,7247757312,-164995463643136,

%T -18446744073709551616,9803356117276277820358656,

%U 24178516392292583494123520000000,-271732164163901599116133024293512544256,-13717048991958695477963985711266803110069141504,3074347100178259797134292590832254504315406543889629184

%N a(n)=(-1)^((n-2)*(n-1)/2)*2^((n-1)^2)*n^(n-3).

%C Discriminant of Pell polynomials.

%C Pell polynomials are defined as P(0)=0, P(1)=1 and P(n)=2xP(n-1)+P(n-2) for n>1.

%H Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, <a href="https://arxiv.org/abs/1808.01264">The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials</a>, arXiv:1808.01264 [math.NT], 2018.

%H Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Florez2/florez8.html">Star of David and other patterns in the Hosoya-like polynomials triangles</a>, 2018.

%H R. Flórez, N. McAnally, and A. Mukherjees, <a href="http://math.colgate.edu/~integers/s18b2/s18b2.Abstract.html">Identities for the generalized Fibonacci polynomial</a>, Integers, 18B (2018), Paper No. A2.

%H R. Flórez, R. Higuita and A. Mukherjees, <a href="http://math.colgate.edu/~integers/s14/s14.Abstract.html">Characterization of the strong divisibility property for generalized Fibonacci polynomials</a>, Integers, 18 (2018), Paper No. A14.

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

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

%t Array[(-1)^((#-2)*(#-1)/2)* 2^((#-1)^2)*#^(#-3)&,15]

%Y Cf. A006645, A001629, A001871, A006645, A007701, A045618, A045925, A093967, A193678, A317404, A317405, A317408, A317451, A318184, A318197.

%Y Essentially the same as A086804.

%K sign

%O 1,3

%A _Rigoberto Florez_, Aug 26 2018

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Last modified April 25 10:01 EDT 2024. Contains 371967 sequences. (Running on oeis4.)