%I #20 Dec 13 2019 05:54:43

%S 1,1,11,151,15619,655177,27085381,2330931341,12157712239,

%T 37307713155613,339781108897078469,75489558096433522049,

%U 11482547005345338463969,3607856726470666022715979,18497593486903125823791655511,520679973964725199436393399689

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

%C The denominators are given in A176366.

%C Bisection of A049330. See it for further references.

%H G. C. Greubel, <a href="/A176365/b176365.txt">Table of n, a(n) for n = 1..75</a>

%H M. R. Darafsheh, Hassan Jolany, <a href="http://arxiv.org/abs/1004.2653">An extension of Lobachevsky formula</a>, arXiv:1004.2653 [math.GM], 2010-2017.

%F a(n) = A049330(2*n).

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

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

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

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

%p A176365 := proc(n) sin(x)^(2*n)/x^(2*n) ; int(%,x=0..infinity)/Pi ; numer(%) ; end proc: # _R. J. Mathar_, Apr 24 2010

%t a[n_]:= (1/Pi)*Integrate[(Sin[x]/x)^(2n), {x, 0, Infinity}]//Numerator; Array[a, 16] (* _Jean-François Alcover_, Nov 25 2017 *)

%Y Cf. A049330, A176366.

%K frac,nonn

%O 1,3

%A _Jonathan Vos Post_, Apr 16 2010

%E 5 terms added and broken URL corrected by _R. J. Mathar_, Apr 24 2010

%E Further terms from _Max Alekseyev_, May 07 2010