A176366 Denominator of (1/Pi)*Integral_{0..infinity} (sin x / x)^(2*n) dx.

2, 3, 40, 630, 72576, 3326400, 148262400, 13621608000, 75277762560, 243290200817664, 2322315553259520000, 538583682060103680000, 85226428809510912000000, 27777728189842735104000000, 147362699895661699242393600000, 4282728465717668134232064000000

Offset: 1

Author

Jonathan Vos Post, Apr 16 2010

Keywords

• frac
• nonn

Comments

The numerators are given in A176365.

Bisection of A049331. See it for further references.

Examples

			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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..75
• 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.

Crossrefs

Cf. A176365.

Programs

Mathematica

a[n_]:= (1/Pi)*Integrate[(Sin[x]/x)^(2n), {x, 0, Infinity}]//Denominator;
Array[a, 16] (* Jean-François Alcover, Nov 25 2017 *)

Formula

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

Extensions

Edited and extended by Max Alekseyev, May 07 2010