A323117 a(n) = T_{n}(n-1) where T_{n}(x) is a Chebyshev polynomial of the first kind.

1, 0, 1, 26, 577, 15124, 470449, 17057046, 708158977, 33165873224, 1730726404001, 99612037019890, 6269617090376641, 428438743526336412, 31592397706723526737, 2500433598371461203374, 211434761022028192051201, 19023879409608991280267536

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..351

Wikipedia, Chebyshev polynomials.

Formula

a(n)^2 - ((n - 1)^2 - 1) * A323118(n-1)^2 = 1 for n > 0.

a(n) = A322836(n,n-1) for n > 0.

a(n) ~ exp(-1) * 2^(n-1) * n^n. - Vaclav Kotesovec, Jan 05 2019

a(n) = cos(n*arccos(n-1)). - Seiichi Manyama, Mar 05 2021

a(n) = n * Sum_{k=0..n} (2*n-4)^k * binomial(n+k,2*k)/(n+k) for n > 0. - Seiichi Manyama, Mar 05 2021

Mathematica

Table[ChebyshevT[n, n - 1], {n, 0, 20}] (* Vaclav Kotesovec, Jan 05 2019 *)

Prog

(PARI) a(n) = polchebyshev(n, 1, n-1);
(PARI) a(n) = round(cos(n*acos(n-1))); \\ Seiichi Manyama, Mar 05 2021
(PARI) a(n) = if(n==0, 1, n*sum(k=0, n, (2*n-4)^k*binomial(n+k, 2*k)/(n+k))); \\ Seiichi Manyama, Mar 05 2021

Crossrefs

Cf. A115066, A322836, A323118.

Sequence in context: A257518 A283343 A160059 * A293612 A197123 A203598

Adjacent sequences: A323114 A323115 A323116 * A323118 A323119 A323120

Keyword

nonn

Author

Seiichi Manyama, Jan 05 2019

Status

approved