A323181 a(n) = U_{2*n-1}(n)/(2*n) where U_{n}(x) is a Chebyshev polynomial of the second kind.

1, 14, 1155, 238204, 92208005, 57723886506, 53303126198791, 68201766898127864, 115562692712642803209, 250568062566458497345990, 676789415690723540731574411, 2228525638897473760683321942900, 8788368165086865758098175776802701, 40895852668226096118083495224349942114

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..194

Wikipedia, Chebyshev polynomials.

Formula

a(n) = U_{n-1}(2*n^2-1).

a(n) = (1/2) * Sum_{k=0..n-1} binomial(2*n,2*k+1)*(n^2-1)^(n-1-k)*n^(2*k).

a(n) ~ 2^(2*n - 2) * n^(2*n - 2). - Vaclav Kotesovec, Jan 07 2019

Mathematica

Table[ChebyshevU[2*n - 1, n]/(2*n), {n, 1, 15}] (* Vaclav Kotesovec, Jan 07 2019 *)

Prog

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

Crossrefs

Cf. A056220, A173194.

Sequence in context: A132504 A178989 A232373 * A206613 A198712 A204972

Adjacent sequences: A323178 A323179 A323180 * A323182 A323183 A323184

Keyword

nonn

Author

Seiichi Manyama, Jan 06 2019

Status

approved