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A323118 a(n) = U_{n}(n) where U_{n}(x) is a Chebyshev polynomial of the second kind. 4
1, 2, 15, 204, 3905, 96030, 2883167, 102213944, 4178507265, 193501094490, 10011386405999, 572335117886532, 35827847605137601, 2437406399741075126, 179059769134174484415, 14127079203550978667760, 1191321539697176278429697, 106935795565608726499866930 (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) = Sum_{k=0..floor(n/2)} binomial(n+1,2*k+1)*(n^2-1)^k*n^(n-2*k).

a(n) ~ 2^n * n^n. - Vaclav Kotesovec, Jan 05 2019

MATHEMATICA

Table[ChebyshevU[n, n], {n, 0, 20}] (* Vaclav Kotesovec, Jan 05 2019 *)

PROG

(PARI) {a(n) = polchebyshev(n, 2, n)}

(PARI) {a(n) = sum(k=0, n\2, binomial(n+1, 2*k+1)*(n^2-1)^k*n^(n-2*k))}

CROSSREFS

Main diagonal of A323182.

Cf. A115066, A318192, A323117.

Sequence in context: A221102 A319466 A020557 * A184361 A124558 A020565

Adjacent sequences:  A323115 A323116 A323117 * A323119 A323120 A323121

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jan 05 2019

STATUS

approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)