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A370261
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a(n) = sqrt(A370259(2*n)/(n+1)) for n >= 1.
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4
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1, 5, 65, 1449, 46561, 1968525, 103565057, 6531391313, 480749649601, 40482981221781, 3840053099665729, 405275779792031225, 47113209228513626017, 5982545638922153790749, 823992221632687352744961, 122360935410018418223907489, 19489013519781051891806113153
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OFFSET
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1,2
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COMMENTS
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The sequence is conjectured to be integral.
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LINKS
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FORMULA
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a(n) = sqrt( (T(2*n, 2*n+1) - 1)/((n+1)*(2*n)^3) ), where T(n, x) is the n-th Chebyshev polynomial of the first kind.
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MAPLE
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A370259 := n -> simplify( (ChebyshevT(n, n+1) - 1)/n^3 ):
seq(sqrt(A370259(2*n)/(n+1)), n = 1..20);
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MATHEMATICA
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Table[Sqrt[(ChebyshevT[2*n, 2*n + 1] - 1)/(2*n)^3/(n + 1)], {n, 20}] (* Paolo Xausa, Jul 24 2024 *)
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PROG
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(Python)
from math import isqrt
from sympy import chebyshevt
def A370261(n): return isqrt((chebyshevt((m:=n<<1), m+1)-1)//((n+1)*m**3)) # Chai Wah Wu, Mar 13 2024
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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