A049330 Numerator of (1/Pi)*Integral_{x=0..infinity} (sin(x)/x)^n dx.

1, 1, 3, 1, 115, 11, 5887, 151, 259723, 15619, 381773117, 655177, 20646903199, 27085381, 467168310097, 2330931341, 75920439315929441, 12157712239, 5278968781483042969, 37307713155613, 9093099984535515162569, 339781108897078469, 168702835448329388944396777

Offset

1,3

Links

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

Ulrich Abel and Vitaliy Kushnirevych, Sinc integrals revisited, Mathematische Semesterberichte (2023).

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]

Iskander Aliev and Martin Henk, Minkowski's successive minima in convex and discrete geometry, arXiv:2304.00120 [math.MG], 2023.

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

Formula

a(n) = numerator( n*A099765(n)/(2^n*(n-1)!) ). - G. C. Greubel, Apr 01 2022

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 *)

Prog

(Magma) [Numerator( (1/(2^n*Factorial(n-1)))*(&+[(-1)^j*Binomial(n, j)*(n-2*j)^(n-1): j in [0..Floor(n/2)]]) ): n in [1..25]]; // G. C. Greubel, Apr 01 2022
(Sage) [numerator( (1/(2^n*factorial(n-1)))*sum((-1)^j*binomial(n, j)*(n-2*j)^(n-1) for j in (0..(n//2))) ) for n in (1..25)] # G. C. Greubel, Apr 01 2022

Crossrefs

Cf. Same as A002297 except for n=4 term, A049331.

Cf. A002304, A002305.

Sequence in context: A352232 A221195 A071291 * A274040 A367948 A369187

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