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

Author

Seiichi Manyama, Mar 05 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..351
• Wikipedia, Chebyshev polynomials.

Crossrefs

Cf. A107995, A115066, A323117, A342205.

Programs

Mathematica

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

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)));

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