OFFSET
1,3
REFERENCES
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.4.3, p. 22.
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
KEYWORD
nonn,frac,easy,nice
AUTHOR
N. J. A. Sloane, Mark S. Riggs (msr1(AT)ra.msstate.edu), Dec 11 1999
STATUS
approved