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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n=1..100

Iskander Aliev, Siegel's Lemma and Sum-Distinct Sets, arXiv:math/0503115 [math.NT] (2005) and  Discrete and Computational Geometry, Volume 39, Numbers 1-3 / 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), 888-901.

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.

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}] (* Jean-François Alcover, Dec 02 2013 *)

Denominator@Table[Sum[(-1)^k (n-2k)^(n-1) Binomial[n, k], {k, 0, n/2}]/((n-1)! 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

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)