A176366 - OEIS

%I #13 Dec 08 2019 20:53:42

%S 2,3,40,630,72576,3326400,148262400,13621608000,75277762560,

%T 243290200817664,2322315553259520000,538583682060103680000,

%U 85226428809510912000000,27777728189842735104000000,147362699895661699242393600000,4282728465717668134232064000000

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

%C The numerators are given in A176365.

%C Bisection of A049331. See it for further references.

%H G. C. Greubel, <a href="/A176366/b176366.txt">Table of n, a(n) for n = 1..75</a>

%H M.R. Darafsheh, Hassan Jolany, <a href="https://arxiv.org/abs/1004.2653v1">Calculating (\int_0^\infty(sin^2n x)/x^2n dx)</a>, arXiv:1004.2653v1 [math.GM], 14 April 2010. Appears in International e-Journal of Engineering Mathematics: Theory and Application, 2009, vol. 7.

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

%e a(2) = 3 because Integral_{0..infinity} (sin(x)/x)^4 dx = (1/3)*Pi.

%e a(3) = 40 because Integral_{0..infinity} (sin(x)/x)^6 dx = (11/40)*Pi.

%e a(4) = 630 because Integral_{0..infinity} (sin(x)/x)^8 dx = (151/630)*Pi.

%e a(5) = 72576 because Integral_{0..infinity} (sin(x)/x)^10 dx = (15619/72576)*Pi.

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

%t Array[a, 16] (* _Jean-François Alcover_, Nov 25 2017 *)

%Y Cf. A176365.

%K frac,nonn

%O 1,1

%A _Jonathan Vos Post_, Apr 16 2010

%E Edited and extended by _Max Alekseyev_, May 07 2010