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A004730
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Numerator of n!!/(n+1)!! (cf. A006882).
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7
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1, 1, 2, 3, 8, 5, 16, 35, 128, 63, 256, 231, 1024, 429, 2048, 6435, 32768, 12155, 65536, 46189, 262144, 88179, 524288, 676039, 4194304, 1300075, 8388608, 5014575, 33554432, 9694845, 67108864, 300540195, 2147483648, 583401555, 4294967296, 2268783825
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OFFSET
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0,3
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LINKS
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FORMULA
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Let y(m) = y(m-2) + 1/y(m-1) for m >= 2, with y(0)=y(1)=1. Then the denominator of y(n+1) equals the numerator of n!!/(n+1)!! for n >= 0, where the double factorials are given by A006882. [Reinhard Zumkeller, Dec 08 2011, as corrected in Cooper (2015)]
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MATHEMATICA
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Numerator[#[[1]]/#[[2]]&/@Partition[Range[0, 40]!!, 2, 1]] (* Harvey P. Dale, Jan 22 2013 *)
Numerator[CoefficientList[Series[(1 - Sqrt[1 - c^2] + ArcSin[c])/(c Sqrt[1 - c^2]), {c, 0, 39}], c]] (* Eugene d'Eon, Nov 01 2018 *)
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PROG
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(Haskell)
import Data.Ratio ((%), denominator)
a004730 n = a004730_list !! n
a004730_list = map denominator ggs where
ggs = 1 : 2 : zipWith (+) ggs (map (1 /) $ tail ggs) :: [Rational]
(Magma) DoubleFactorial:=func< n | &*[n..2 by -2] >; [ Numerator(DoubleFactorial(n) / DoubleFactorial(n+1)): n in [0..35]]; // Vincenzo Librandi, Dec 03 2018
(Python)
from sympy import gcd, factorial2
a, b = factorial2(n), factorial2(n+1)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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