login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A176366 Denominator of (1/Pi)*Integral_{0..inf} (sin x / x)^(2*n) dx. 1
2, 3, 40, 630, 72576, 3326400, 148262400, 13621608000, 75277762560, 243290200817664, 2322315553259520000, 538583682060103680000, 85226428809510912000000, 27777728189842735104000000, 147362699895661699242393600000, 4282728465717668134232064000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The numerators are given in A176365.

Bisection of A049331. See it for further references.

LINKS

Table of n, a(n) for n=1..16.

M.R. Darafsheh, Hassan Jolany, Calculating (\int_0^\infty(sin^2n x)/x^2n dx), arXiv:1004.2653v1 [math.GM], 14 April 2010. Appears in International e-Journal of Engineering Mathematics: Theory and Application, 2009, vol. 7.

FORMULA

a(n) = A049331(2*n).

EXAMPLE

a(2) = 3 because Integral[0..infinity] (sin(x)/x)^4 dx = (1/3)Pi.

a(3) = 40 because Integral[0..infinity] (sin(x)/x)^6 dx = (11/40)Pi.

a(4) = 630 because Integral[0..infinity] (sin(x)/x)^8 dx = (151/630)Pi.

a(5) = 72576 because Integral[0..infinity] (sin(x)/x)^10 dx = (15619/72576)Pi.

MATHEMATICA

a[n_] := 1/Pi Integrate[(Sin[x]/x)^(2n), {x, 0, Infinity}] // Denominator;

Array[a, 16] (* Jean-Fran├žois Alcover, Nov 25 2017 *)

CROSSREFS

Cf. A176365.

Sequence in context: A088984 A097170 A231797 * A157132 A262189 A077336

Adjacent sequences:  A176363 A176364 A176365 * A176367 A176368 A176369

KEYWORD

frac,nonn

AUTHOR

Jonathan Vos Post, Apr 16 2010

EXTENSIONS

Edited and extended by Max Alekseyev, May 07 2010

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 February 15 16:53 EST 2019. Contains 320136 sequences. (Running on oeis4.)