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%I #37 Jan 04 2024 18:10:01
%S 1,144,629856,69657034752,178523361331200000,
%T 10072680467275913619308544,12094526244510115670028303294529536,
%U 301689370251168256106930569591201258430005248,153543958878683931150976515367278080485732740052794998784,1572290138917723454985999517360927544173903258140620787548160000000000
%N a(n) = 2^((n - 1)*(n + 2)/2)*3^(n*(n - 1))*n^n.
%C Discriminant of Fermat-Lucas polynomials.
%C Fermat-Lucas polynomials are defined as F(0) = 2, F(1) = 3*x and F(n) = 3*x*F(n - 1) - 2*F(n - 2) for n > 1.
%H Andrew Howroyd, <a href="/A318197/b318197.txt">Table of n, a(n) for n = 1..30</a>
%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 R. Flórez, R. Higuita, and A. Mukherjee, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Florez2/florez8.html">The Star of David and Other Patterns in Hosoya Polynomial Triangles</a>, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
%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/Fermat-LucasPolynomial.html">Fermat-Lucas polynomials</a>
%t Array[2^((# - 1) (# + 2)/2)*3^(# (# - 1))*#^# &, 10] (* _Michael De Vlieger_, Aug 22 2018 *)
%o (PARI) apply(poldisc, Vec((2-3*x*y)/(1-3*y*x+2*x^2) - 2 + O(x^12))) \\ _Andrew Howroyd_, Aug 20 2018
%o (PARI) a(n) = 2^((n - 1)*(n + 2)/2)*3^(n*(n - 1))*n^n; \\ _Andrew Howroyd_, Aug 20 2018
%o (Magma) [2^((n - 1)*(n + 2) div 2)*3^(n*(n - 1))*n^n: n in [1..10]]; // _Vincenzo Librandi_, Aug 25 2018
%Y Cf. A137372, A193678, A007701, A007701, A193678.
%K nonn
%O 1,2
%A _Rigoberto Florez_, Aug 20 2018
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