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A334124
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a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{2*n}(i*x/2))), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1).
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2
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1, 3, 71, 17753, 46069729, 1234496016491, 341133743251787719, 971684488369988888850993, 28523907708086181923163934073729, 8628515016553040037389969912341438652243, 26895841132028233579514694272575933932911355677831
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ 2^(1/4) * exp(2*G*n*(2*n+1)/Pi) / (1 + sqrt(2))^n, where G is Catalan's constant A006752. - Vaclav Kotesovec, Apr 16 2020, updated Jan 03 2021
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MATHEMATICA
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Table[2^n * Sqrt[Resultant[ChebyshevU[2*n, x/2], ChebyshevT[2*n, I*x/2], x]], {n, 0, 12}] (* Vaclav Kotesovec, Apr 16 2020 *)
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PROG
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(PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(2*n, 1, I*x/2)))}
(Python)
from math import isqrt
from sympy import resultant, chebyshevt, chebyshevu, I
from sympy.abc import x
def A334124(n): return isqrt(resultant(chebyshevu(n<<1, x/2), chebyshevt(n<<1, I*x/2))*(1<<(n<<1))) if n else 1 # Chai Wah Wu, Nov 07 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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