A243133 64*n^7 - 112*n^5 + 56*n^3 - 7*n.

0, 1, 5042, 114243, 937444, 4656965, 17057046, 50843527, 130576328, 299537289, 628855930, 1229215691, 2265463212, 3974443213, 6686381534, 10850138895, 17062657936, 26102926097, 38970776898, 56930852179, 81562047860, 114812765781, 159062294182

Offset: 0

Author

Vincenzo Librandi, May 31 2014

Keywords

• nonn
• easy

Comments

Chebyshev polynomial of the first kind T(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. A056220, A144129, A144130.

Programs

Magma

[64*n^7-112*n^5+56*n^3-7*n: n in [0..40]];

Mathematica

Table[ChebyshevT[7, n], {n, 0, 40}] (* or *)  Table[64 n^7 - 112 n^5 + 56 n^3 - 7 n, {n, 0, 40}]
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,1,5042,114243,937444,4656965,17057046,50843527},40] (* Harvey P. Dale, Mar 27 2015 *)

Formula

G.f.: (x + 5034*x^2 + 73935*x^3 + 164620*x^4 + 73935*x^5 + 5034*x^6 + x^7)/(1 - x)^8.

a(n) = n*(64*n^6 - 112*n^4 + 56*n^2 - 7).

a(0)=0, a(1)=1, a(2)=5042, a(3)=114243, a(4)=937444, a(5)=4656965, a(6)=17057046, a(7)=50843527, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)- 70*a(n-4)+ 56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8). - Harvey P. Dale, Mar 27 2015