A322899 a(n) = T_{2*n}(n+1) where T_{n}(x) is a Chebyshev polynomial of the first kind.

1, 7, 577, 119071, 46099201, 28860511751, 26650854921601, 34100354867927167, 57780789062419261441, 125283240358674708816199, 338393251269110482793304001, 1114259437504123772777608493087, 4394174409561746573589926449440001

Offset: 0

Author

Seiichi Manyama, Dec 30 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..193
• Wikipedia, Chebyshev polynomials.
• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Diagonal of A188644.

Programs

Mathematica

a[n_] := ChebyshevT[2n, n+1];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Jan 02 2019 *)

PARI

{a(n) = polchebyshev(2*n, 1, n+1)}

PARI

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

Formula

a(n) = T_{n}(2*n^2+4*n+1).

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

a(n) ~ exp(2) * 2^(2*n-1) * n^(2*n). - Vaclav Kotesovec, Apr 15 2020