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A049330 Numerator of (1/Pi)*Integral_{0..inf} (sin x / x)^n dx. 6
1, 1, 3, 1, 115, 11, 5887, 151, 259723, 15619, 381773117, 655177, 20646903199, 27085381, 467168310097, 2330931341, 75920439315929441, 12157712239, 5278968781483042969, 37307713155613, 9093099984535515162569 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The subsequence of primes in the unsorted order of occurrence begins (through n=100, the last and largest in that range has n=63): 3, 11, 151, 259723, 15619, 27085381, 3607856726470666022715979, 162393536899851293236257827401317071582797663083205707005010585853997149812190935313632896689565597 - Jonathan Vos Post, Feb 05 2011

LINKS

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

Iskander Aliev, Siegel's Lemma and Sum-Distinct Sets, (2005) arXiv:math/0503115 [math.NT]; 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

Numerator[Table[Integrate[(Sin[x]/x)^n, {x, 0, \[Infinity]}]/Pi, {n, 25}]] (* Harvey P. Dale, Jan 01 2013 *)

Numerator@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. A049331. Same as A002297 except for n=4 term. Cf. also A002304, A002305.

Sequence in context: A241191 A221195 A071291 * A274040 A266363 A068542

Adjacent sequences:  A049327 A049328 A049329 * A049331 A049332 A049333

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 14 17:58 EST 2019. Contains 329979 sequences. (Running on oeis4.)