A318192 a(n) = U_{n}(n)/(n+1) where U_{n}(x) is a Chebyshev polynomial of the second kind.

1, 1, 5, 51, 781, 16005, 411881, 12776743, 464278585, 19350109449, 910126036909, 47694593157211, 2755988277318277, 174100457124362509, 11937317942278298961, 882942450221936166735, 70077737629245663437041, 5940877531422707027770385

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..352

Wikipedia, Chebyshev polynomials.

Formula

a(n) = A323118(n)/(n+1).

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

Prog

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

Crossrefs

Cf. A323118.

Sequence in context: A339234 A187235 A343674 * A343687 A299435 A095839

Adjacent sequences: A318189 A318190 A318191 * A318193 A318194 A318195

Keyword

nonn

Author

Seiichi Manyama, Jan 07 2019

Status

approved