login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004730 Numerator of n!!/(n+1)!! (cf. A006882). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

S. Janson, On the traveling fly problem, Graph Theory Notes of New York, Vol. XXXI, 17, 1996.

LINKS

T. D. Noe, Table of n, a(n) for n=0..300

Joseph E. Cooper III, A recurrence for an expression involving double factorials, arXiv:1510.00399 [math.CO], 2015.

S. Janson, On the traveling fly problem

FORMULA

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)]

MATHEMATICA

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 *)

PROG

(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]

-- Reinhard Zumkeller, Dec 08 2011

(MAGMA) DoubleFactorial:=func< n | &*[n..2 by -2] >; [ Numerator(DoubleFactorial(n) / DoubleFactorial(n+1)): n in [0..35]]; // Vincenzo Librandi, Dec 03 2018

CROSSREFS

Cf. A004731, A006882 (double factorials).

Sequence in context: A130479 A272878 A094181 * A332460 A168014 A050369

Adjacent sequences:  A004727 A004728 A004729 * A004731 A004732 A004733

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 9 14:08 EDT 2020. Contains 335543 sequences. (Running on oeis4.)