A002297 Numerator of (2/Pi)*Integral_{0..inf} (sin x / x)^n dx.

1, 1, 3, 2, 115, 11, 5887, 151, 259723, 15619, 381773117, 655177, 20646903199, 27085381, 467168310097, 2330931341, 75920439315929441, 12157712239, 5278968781483042969, 37307713155613, 9093099984535515162569, 339781108897078469, 168702835448329388944396777

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy
• nice

Examples

			1, 1, 3/4, 2/3, 115/192, 11/20, ...
		

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n=1..100
• A. H. R. Grimsey, On the accumulation of chance effects and the Gaussian frequency distribution, Phil. Mag., 36 (1945), 294-295.
• R. G. Medhurst and J. H. Roberts, Evaluation of the integral I_n(b) = (2/Pi)*Integral_{0..inf} (sin x / x)^n cos (bx) dx, Math. Comp., 19 (1965), 113-117.

Crossrefs

Cf. A002298 (for denominators), A002304, A002305. Essentially the same as A049330, except for the n=4 term.

Programs

Mathematica

a[n_] := Numerator[ (2/Pi)*Integrate[ (Sin[x]/x)^n, {x, 0, Infinity}] ]; Table[ a[n], {n, 1, 21}] (* Jean-François Alcover, Dec 19 2011 *)
Numerator@Table[Sum[(-1)^k (n-2k)^(n-1) Binomial[n, k], {k, 0, n/2}]/((n-1)! 2^(n-1)), {n, 1, 30}] (* Vladimir Reshetnikov, Sep 02 2016 *)

PARI

a(n) = numerator((n/2^(n-1)) * sum(r=0, n/2, (-1)^r*(n-2*r)^(n-1)/(r!*(n-r)!))); \\ Michel Marcus, Oct 02 2013

Formula

a(n) = numerator((n/2^(n-1)) * sum((-1)^r*(n-2*r)^(n-1)/(r!*(n-r)!), r=0..n/2)). - Sean A. Irvine, Oct 01 2013

Extensions

a(22)-a(23) from T. D. Noe, Feb 22 2014