A242850 a(n) = 32*n^5 - 32*n^3 + 6*n.

0, 6, 780, 6930, 30744, 96030, 241956, 526890, 1032240, 1866294, 3168060, 5111106, 7907400, 11811150, 17122644, 24192090, 33423456, 45278310, 60279660, 79015794, 102144120, 130395006, 164575620, 205573770, 254361744, 312000150, 379641756, 458535330, 550029480, 655576494

Offset

0,2

Comments

Chebyshev polynomial of the second kind U(5,n).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: 6*x*(1 + 124*x + 390*x^2 + 124*x^3 + x^4)/(1 - x)^6.

a(n) = 2*n*(2*n - 1)*(2*n + 1)*(4*n^2 - 3).

From Elmo R. Oliveira, Jul 06 2026: (Start)

E.g.f.: 2*exp(x)*x*(3 + 192*x + 384*x^2 + 160*x^3 + 16*x^4).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). (End)

Mathematica

Table[32 n^5 - 32 n^3 + 6 n, {n, 0, 40}]
(* Alternative: *)
Table[ChebyshevU[5, n], {n, 0, 40}]

Prog

(Magma) [32*n^5-32*n^3+6*n: n in [0..40]];

Crossrefs

Cf. A000466, A144138, A144139, A242851.

Sequence in context: A332176 A382362 A088217 * A364273 A020542 A045480

Adjacent sequences: A242847 A242848 A242849 * A242851 A242852 A242853

Keyword

nonn,easy

Author

Vincenzo Librandi, May 29 2014

Extensions

Edited by Bruno Berselli, May 29 2014

Status

approved