A243132 32*n^6 - 48*n^4 + 18*n^2 - 1.

-1, 1, 1351, 19601, 119071, 470449, 1431431, 3650401, 8193151, 16692641, 31521799, 55989361, 94558751, 153090001, 239104711, 362074049, 533729791, 768398401, 1083358151, 1499219281, 2040327199, 2735188721, 3616921351, 4723725601, 6099380351, 7793761249

Offset: 0

Author

Vincenzo Librandi, May 31 2014

Keywords

• sign
• easy

Comments

Chebyshev polynomial of the first kind T(6,n).

Links

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

Crossrefs

Cf. A056220, A144129, A144130.

Programs

Magma

[32*n^6-48*n^4+18*n^2-1: n in [0..40]];

Mathematica

Table[ChebyshevT[6, n], {n, 0, 40}] (* or *) Table[32 n^6 - 48 n^4 + 18 n^2 - 1, {n, 0, 20}]

Formula

G.f.: (-1 + 8*x + 1323*x^2 + 10200*x^3 + 10165*x^4 + 1344*x^5 + x^6)/(1 - x)^7.

a(n) = (2*n^2 - 1)*(16*n^4 - 16*n^2 + 1).