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A342205 a(n) = T(n,n+1) where T(n,x) is a Chebyshev polynomial of the first kind. 5
1, 2, 17, 244, 4801, 120126, 3650401, 130576328, 5374978561, 250283080090, 13007560326001, 746411226303612, 46873096812360001, 3197490648645613334, 235451028081583642049, 18614381236112230383376, 1572584048032918633353217 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..351

Wikipedia, Chebyshev polynomials.

FORMULA

a(n) = cos(n*arccos(n+1)).

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

MATHEMATICA

Table[ChebyshevT[n, n + 1], {n, 0, 16}] (* Amiram Eldar, Mar 05 2021 *)

PROG

(PARI) a(n) = polchebyshev(n, 1, n+1);

(PARI) a(n) = round(cos(n*acos(n+1)));

(PARI) a(n) = if(n==0, 1, n*sum(k=0, n, (2*n)^k*binomial(n+k, 2*k)/(n+k)));

CROSSREFS

Cf. A115066, A323117, A342206, A342207.

Sequence in context: A036082 A240999 A319947 * A099694 A099698 A218681

Adjacent sequences:  A342202 A342203 A342204 * A342206 A342207 A342208

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 05 2021

STATUS

approved

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)