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

0,1

Links

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

Wikipedia, Chebyshev polynomials.

Formula

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

Mathematica

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

Prog

(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)));

Crossrefs

Main diagonal of A299741.

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

Sequence in context: A154750 A041167 A294380 * A308128 A006279 A041521

Adjacent sequences: A343258 A343259 A343260 * A343262 A343263 A343264

Keyword

nonn

Author

Seiichi Manyama, Apr 09 2021

Status

approved