A343261 a(n) = 2 * T(n,(n+2)/2) where T(n,x) is a Chebyshev polynomial of the first kind.

2, 3, 14, 110, 1154, 15127, 238142, 4379769, 92198402, 2186871698, 57721023502, 1678243366813, 53301709843202, 1836220544383695, 68200709735854334, 2716906424134261502, 115561578124838522882, 5227260815326346060059, 250566480717349417632398

Offset: 0

Author

Seiichi Manyama, Apr 09 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386
• Wikipedia, Chebyshev polynomials.

Crossrefs

Main diagonal of A299741.

Cf. A115066, A342167, A342206, A343259, A343260.

Programs

Mathematica

Table[2*ChebyshevT[n, (n+2)/2], {n, 0, 18}] (* Amiram Eldar, Apr 09 2021 *)

PARI

a(n) = 2*polchebyshev(n, 1, (n+2)/2);

PARI

a(n) = round(2*cos(n*acos((n+2)/2)));

PARI

a(n) = if(n==0, 2, 2*n*sum(k=0, n, n^k*binomial(n+k, 2*k)/(n+k)));

Formula

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

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

a(n) ~ exp(2) * n^n. - Vaclav Kotesovec, Apr 09 2021