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

0,1

Links

Seiichi Manyama, Table of n, a(n) for n = 0..386

Wikipedia, Chebyshev polynomials.

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

Mathematica

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

Prog

(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)));

Crossrefs

Main diagonal of A298675.

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

Sequence in context: A271225 A349563 A115507 * A173252 A051502 A228690

Adjacent sequences: A343256 A343257 A343258 * A343260 A343261 A343262

Keyword

nonn

Author

Seiichi Manyama, Apr 09 2021

Status

approved