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

1, 1, -16, -2048, 1638400, 7247757312, -164995463643136, -18446744073709551616, 9803356117276277820358656, 24178516392292583494123520000000, -271732164163901599116133024293512544256, -13717048991958695477963985711266803110069141504, 3074347100178259797134292590832254504315406543889629184

Offset

1,3

Comments

Discriminant of Pell polynomials.

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

Links

Table of n, a(n) for n=1..13.

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, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.

R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.

Eric Weisstein's World of Mathematics, Discriminant

Eric Weisstein's World of Mathematics, Pell Polynomial

Mathematica

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

Crossrefs

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

Essentially the same as A086804.

Sequence in context: A159389 A291828 A086804 * A121366 A101800 A208148

Adjacent sequences: A317447 A317448 A317449 * A317451 A317452 A317453

Keyword

sign

Author

Rigoberto Florez, Aug 26 2018

Status

approved