A322747 a(n) = sqrt(1 + A322746(2*n)).

1, 5, 161, 8749, 665857, 65160501, 7793761249, 1101696200669, 179689877047297, 33215554576822501, 6862186181491284001, 1566923219786361397005, 391868347839681254572801, 106523078497331434142611733, 31273034455313887578671676257

Offset: 0

Author

Seiichi Manyama, Dec 25 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..296
• Wikipedia, Chebyshev polynomials.
• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Cf. A322746, A322790.

Programs

PARI

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

PARI

{a(n) = polchebyshev(n, 1, 4*n+1)}

Formula

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

a(n) = A322790(2*n, n).

a(n) = T_{n}(4*n+1) where T_{n}(x) is a Chebyshev polynomial of the first kind.

a(n) ~ exp(1/4) * 2^(3*n - 1) * n^n. - Vaclav Kotesovec, Dec 25 2018