A242850 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

Author

Vincenzo Librandi, May 29 2014

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A000466, A144138, A144139, A242851.

Programs

Magma

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

Mathematica

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

Formula

G.f.: x*(6 + 744*x + 2340*x^2 + 744*x^3 + 6*x^4)/(1 - x)^6.

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

Extensions

Edited by Bruno Berselli, May 29 2014