A349071 a(n) = T(n, 2*n), where T(n, x) is the Chebyshev polynomial of the first kind.
1, 2, 31, 846, 32257, 1580050, 94558751, 6686381534, 545471324161, 50428155189474, 5210183616019999, 594949288292777902, 74404881332329766401, 10114032809617941274226, 1484781814660796486716447, 234114571438498509048719550, 39459584112457284328544403457
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..321
- Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind.
- Wikipedia, Chebyshev polynomials.
Programs
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Mathematica
Table[ChebyshevT[n, 2*n], {n, 0, 20}] -
PARI
a(n) = polchebyshev(n, 1, 2*n); \\ Michel Marcus, Nov 07 2021
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Python
from sympy import chebyshevt def A349071(n): return chebyshevt(n,n<<1) # Chai Wah Wu, Nov 08 2023
Formula
a(n) = cosh(n*arccosh(2*n)).
a(n) = ((2*n + sqrt(4*n^2-1))^n + (2*n - sqrt(4*n^2-1))^n)/2.
a(n) ~ 2^(2*n-1) * n^n.