A242852 128*n^7-192*n^5+80*n^3-8*n.

0, 8, 10864, 235416, 1905632, 9409960, 34356048, 102213944, 262184896, 600940872, 1260879920, 2463542488, 4538833824, 7960697576, 13389885712, 21724469880, 34158739328, 52251130504, 78001833456, 113940720152, 163226239840, 229755926568, 318289163984, 434582852536

Offset: 0

Author

Vincenzo Librandi, May 30 2014

Keywords

• nonn
• easy

Comments

Chebyshev polynomial of the second kind U(7,n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A144138, A144139, A242850, A242851.

Programs

Magma

[128*n^7-192*n^5+80*n^3-8*n: n in [0..30]];

Mathematica

Table[ChebyshevU[7, n], {n, 0, 30}] (* or *) Table[128 n^7 - 192 n^5 + 80 n^3 - 8 n, {n, 0, 30}]

Formula

G.f.: (8*x + 10800*x^2 + 148728*x^3 + 326048*x^4 + 148728*x^5 + 10800*x^6 + 8*x^7)/(1-x)^8.

a(n) = 8*n*(2*n^2-1)*(8*n^4-8*n^2+1).