A343259 a(n) = 2 * T(n,n/2) where T(n,x) is a Chebyshev polynomial of the first kind.

2, 1, 2, 18, 194, 2525, 39202, 710647, 14760962, 345946302, 9034502498, 260219353691, 8195978831042, 280256592535933, 10340256951198914, 409468947059131650, 17322711762013765634, 779742677038695037937, 37210469265847998489922, 1876572071974094803391179

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 A298675.

Cf. A097690, A115066, A342205, A343260, A343261.

Programs

Mathematica

Table[2*ChebyshevT[n, n/2], {n, 1, 20}] (* Amiram Eldar, Apr 09 2021 *)

PARI

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

PARI

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

PARI

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

Formula

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

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

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