A176365 Numerator of (1/Pi)*Integral_{0..infinity} (sin x / x)^(2*n) dx.

1, 1, 11, 151, 15619, 655177, 27085381, 2330931341, 12157712239, 37307713155613, 339781108897078469, 75489558096433522049, 11482547005345338463969, 3607856726470666022715979, 18497593486903125823791655511, 520679973964725199436393399689

Offset: 1

Author

Jonathan Vos Post, Apr 16 2010

Keywords

• frac
• nonn

Comments

The denominators are given in A176366.

Bisection of A049330. See it for further references.

Examples

			a(2) = 1 because Integral_{0..infinity} (sin(x)/x)^4 dx = (1/3)*Pi.
a(3) = 11 because Integral_{0..infinity} (sin(x)/x)^6 dx = (11/40)*Pi.
a(4) = 151 because Integral_{0..infinity} (sin(x)/x)^8 dx = (151/630)*Pi.
a(5) = 15619 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, An extension of Lobachevsky formula, arXiv:1004.2653 [math.GM], 2010-2017.

Crossrefs

Cf. A049330, A176366.

Programs

Maple

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

Mathematica

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

Formula

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

Extensions

5 terms added and broken URL corrected by R. J. Mathar, Apr 24 2010

Further terms from Max Alekseyev, May 07 2010