

A049331


Denominator of (1/Pi)*Integral_{0..inf} (sin x / x)^n dx.


5



2, 2, 8, 3, 384, 40, 23040, 630, 1146880, 72576, 1857945600, 3326400, 108999475200, 148262400, 2645053931520, 13621608000, 457065319366656000, 75277762560, 33566877054287216640, 243290200817664
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OFFSET

1,1


LINKS

T. D. Noe, Table of n, a(n) for n=1..100
Iskander Aliev, Siegel's Lemma and SumDistinct Sets, arXiv:math/0503115 [math.NT] (2005) and Discrete and Computational Geometry, Volume 39, Numbers 13 / March, 2008. [Added by N. J. A. Sloane, Jul 09 2009]
R. Baillie, D. Borwein and J. M. Borwein, Surprising Sinc Sums and Integrals, Amer. Math. Monthly, 115 (2008), 888901.
A. H. R. Grimsey, On the accumulation of chance effects and the Gaussian frequency distribution, Phil. Mag., 36 (1945), 294295.
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), 113117.
Eric Weisstein's World of Mathematics, Sinc Function


EXAMPLE

1/2, 1/2, 3/8, 1/3, 115/384, 11/40, ...


MATHEMATICA

Table[ 1/Pi*Integrate[Sinc[x]^n, {x, 0, Infinity}] // Denominator, {n, 1, 20}] (* JeanFrançois Alcover, Dec 02 2013 *)
Denominator@Table[Sum[(1)^k (n2k)^(n1) Binomial[n, k], {k, 0, n/2}]/((n1)! 2^n), {n, 1, 30}] (* Vladimir Reshetnikov, Sep 02 2016 *)


CROSSREFS

Cf. A049330. Twice A002298, except for n=4 term. Cf. also A002304, A002305.
Sequence in context: A093731 A195361 A274041 * A239677 A331333 A120399
Adjacent sequences: A049328 A049329 A049330 * A049332 A049333 A049334


KEYWORD

nonn,frac,easy,nice


AUTHOR

N. J. A. Sloane, Mark S. Riggs (msr1(AT)ra.msstate.edu), Dec 11 1999


STATUS

approved



