

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
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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 SumDistinct Sets, (2005) arXiv:math/0503115 [math.NT]; 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

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



