A342206 a(n) = T(n,n+2) where T(n,x) is a Chebyshev polynomial of the first kind.

1, 3, 31, 485, 10081, 262087, 8193151, 299537289, 12545596801, 592479412811, 31154649926687, 1805486216133613, 114342125644787041, 7857107443850071695, 582268591681887560191, 46292552162781456490001, 3930448770533424343942657

Offset

0,2

Links

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

Wikipedia, Chebyshev polynomials.

Formula

a(n) = cos(n*arccos(n+2)).

a(n) = n * Sum_{k=0..n} (2*n+2)^k * binomial(n+k,2*k)/(n+k) for n > 0.

a(n) ~ exp(2) * 2^(n-1) * n^n. - Vaclav Kotesovec, Mar 12 2024

Mathematica

Table[ChebyshevT[n, n + 2], {n, 0, 16}] (* Amiram Eldar, Mar 05 2021 *)

Prog

(PARI) a(n) = polchebyshev(n, 1, n+2);
(PARI) a(n) = round(cos(n*acos(n+2)));
(PARI) a(n) = if(n==0, 1, n*sum(k=0, n, (2*n+2)^k*binomial(n+k, 2*k)/(n+k)));

Crossrefs

Cf. A107995, A115066, A323117, A342205.

Sequence in context: A142999 A212917 A223993 * A346313 A143637 A327227

Adjacent sequences: A342203 A342204 A342205 * A342207 A342208 A342209

Keyword

nonn

Author

Seiichi Manyama, Mar 05 2021

Status

approved