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A323117 a(n) = T_{n}(n-1) where T_{n}(x) is a Chebyshev polynomial of the first kind. 4
1, 0, 1, 26, 577, 15124, 470449, 17057046, 708158977, 33165873224, 1730726404001, 99612037019890, 6269617090376641, 428438743526336412, 31592397706723526737, 2500433598371461203374, 211434761022028192051201, 19023879409608991280267536 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 20 01:55 EDT 2021. Contains 343118 sequences. (Running on oeis4.)