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A002297 Numerator of (2/Pi)*Integral_{0..inf} (sin x / x)^n dx.
(Formerly M2262 N0893)

%I M2262 N0893

%S 1,1,3,2,115,11,5887,151,259723,15619,381773117,655177,20646903199,

%T 27085381,467168310097,2330931341,75920439315929441,12157712239,

%U 5278968781483042969,37307713155613,9093099984535515162569,339781108897078469,168702835448329388944396777

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

%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="/A002297/b002297.txt">Table of n, a(n) for n=1..100</a>

%H A. H. R. Grimsey, <a href="http://dx.doi.org/10.1080/14786444508521508">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.

%F 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

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

%t a[n_] := Numerator[ (2/Pi)*Integrate[ (Sin[x]/x)^n, {x, 0, Infinity}] ]; Table[ a[n], {n, 1, 21}] (* _Jean-Fran├žois Alcover_, Dec 19 2011 *)

%t 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 *)

%o (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

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

%K nonn,frac,easy,nice

%O 1,3

%A _N. J. A. Sloane_

%E a(22)-a(23) from _T. D. Noe_, Feb 22 2014

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Last modified December 6 06:34 EST 2019. Contains 329784 sequences. (Running on oeis4.)