login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A049330 Numerator of (1/Pi)*Integral_{x=0..infinity} (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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)