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Denominator of (2/Pi)*Integral_{0..inf} (sin x / x)^n dx.
(Formerly M3217 N1303)
5

%I M3217 N1303 #32 Jan 11 2018 01:09:01

%S 1,1,4,3,192,20,11520,315,573440,36288,928972800,1663200,54499737600,

%T 74131200,1322526965760,6810804000,228532659683328000,37638881280,

%U 16783438527143608320,121645100408832,30370031620545576960000

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

%C Except for the n=4 term, equal to A049331/2.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H T. D. Noe, <a href="/A002298/b002298.txt">Table of n, a(n) for n=1..100</a>

%H A. H. R. Grimsey, <a href="http://www.tandfonline.com/doi/abs/10.1080/14786444508521508#.U7-EnG2fUTA">On the accumulation of chance effects and the Gaussian frequency distribution</a>, Phil. Mag., 36 (1945), 294-295.

%H R. G. Medhurst and J. H. Roberts, <a href="http://dx.doi.org/10.1090/S0025-5718-1965-0172446-8">Evaluation of the integral I_n(b) = (2/Pi)*Integral_{0..inf} (sin x / x)^n cos (bx) dx</a>, Math. Comp., 19 (1965), 113-117.

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

%t Denominator[Table[2/Pi Integrate[(Sin[x]/x)^n,{x,0,\[Infinity]}],{n,25}]] (* _Harvey P. Dale_, Sep 04 2011 *)

%t 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 *)

%Y Cf. A002297, A002304, A002305.

%K nonn,frac,easy,nice

%O 1,3

%A _N. J. A. Sloane_

%E Corrected and extended by Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 02 2001