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A052469
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Denominators in the Taylor series for arccosh(x) - log(2*x).
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4
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4, 32, 96, 1024, 2560, 4096, 28672, 524288, 1179648, 5242880, 11534336, 100663296, 218103808, 939524096, 134217728, 68719476736, 146028888064, 206158430208, 1305670057984, 2199023255552, 7696581394432, 96757023244288, 202310139510784, 1125899906842624
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OFFSET
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1,1
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REFERENCES
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Bronstein-Semendjajew, sprawotchnik po matematikje, 6th Russian ed. 1956, ch. 4.2.6.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Inverse Hyperbolic Cosecant
Eric Weisstein's World of Mathematics, Inverse Hyperbolic Cosine
Eric Weisstein's World of Mathematics, Inverse Hyperbolic Sine
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FORMULA
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A052468(n) / a(n) = A001147(n) / ( A000165(n) *2*n )
From Johannes W. Meijer, Jul 06 2009: (Start)
a(n) = denom((2*n-1)!/( 4^n * (n!)^2)).
Equals 2*A162442(n+1) for n >= 1.
A052468(n)/a(n) = (1/(2*n))*A001790(n)/A046161(n) for n>=1.
(End)
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EXAMPLE
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arccosh(x) = log(2x) - 1/(4*x^2) - 3/(32*x^4) - 5/(96*x^6) - ... for x>1.
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MATHEMATICA
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a[n_] := Denominator[(2*n-1)!/(2^(2*n)*n!^2)]; Array[a, 21] (* Jean-François Alcover, May 17 2017 *)
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PROG
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(MAGMA) [Denominator(Factorial(2*n-1)/( 2^(2*n)* Factorial(n)^2)): n in [1..30]]; // Vincenzo Librandi, Jul 10 2017
(PARI) {a(n) = denominator((2*n-1)!/(4^n*(n!)^2))}; \\ G. C. Greubel, May 18 2019
(Sage) [denominator(factorial(2*n-1)/(4^n*(factorial(n))^2)) for n in (1..30)] # G. C. Greubel, May 18 2019
(GAP) List([1..30], n-> DenominatorRat( Factorial(2*n-1)/(4^n*(Factorial(n))^2) )) # G. C. Greubel, May 18 2019
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CROSSREFS
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Cf. A002595.
Sequence in context: A153794 A222326 A108914 * A211625 A211630 A211626
Adjacent sequences: A052466 A052467 A052468 * A052470 A052471 A052472
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Updated by Frank Ellermann, May 22 2001
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STATUS
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approved
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