A323117 a(n) = T_{n}(n-1) where T_{n}(x) is a Chebyshev polynomial of the first kind.
1, 0, 1, 26, 577, 15124, 470449, 17057046, 708158977, 33165873224, 1730726404001, 99612037019890, 6269617090376641, 428438743526336412, 31592397706723526737, 2500433598371461203374, 211434761022028192051201, 19023879409608991280267536
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..351
- Wikipedia, Chebyshev polynomials.
Programs
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Mathematica
Table[ChebyshevT[n, n - 1], {n, 0, 20}] (* Vaclav Kotesovec, Jan 05 2019 *) -
PARI
a(n) = polchebyshev(n, 1, n-1);
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PARI
a(n) = round(cos(n*acos(n-1))); \\ Seiichi Manyama, Mar 05 2021
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PARI
a(n) = if(n==0, 1, n*sum(k=0, n, (2*n-4)^k*binomial(n+k, 2*k)/(n+k))); \\ Seiichi Manyama, Mar 05 2021
Formula
a(n)^2 - ((n - 1)^2 - 1) * A323118(n-1)^2 = 1 for n > 0.
a(n) = A322836(n,n-1) for n > 0.
a(n) ~ exp(-1) * 2^(n-1) * n^n. - Vaclav Kotesovec, Jan 05 2019
a(n) = cos(n*arccos(n-1)). - Seiichi Manyama, Mar 05 2021
a(n) = n * Sum_{k=0..n} (2*n-4)^k * binomial(n+k,2*k)/(n+k) for n > 0. - Seiichi Manyama, Mar 05 2021