A002298 Denominator of (2/Pi)*Integral_{0..inf} (sin x / x)^n dx.
1, 1, 4, 3, 192, 20, 11520, 315, 573440, 36288, 928972800, 1663200, 54499737600, 74131200, 1322526965760, 6810804000, 228532659683328000, 37638881280, 16783438527143608320, 121645100408832, 30370031620545576960000
Offset: 1
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.
Programs
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Mathematica
Denominator[Table[2/Pi Integrate[(Sin[x]/x)^n,{x,0,\[Infinity]}],{n,25}]] (* Harvey P. Dale, Sep 04 2011 *) Denominator@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 *)
Extensions
Corrected and extended by Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 02 2001
Comments