This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049330 #66 May 30 2025 11:01:35
%S A049330 1,1,3,1,115,11,5887,151,259723,15619,381773117,655177,20646903199,
%T A049330 27085381,467168310097,2330931341,75920439315929441,12157712239,
%U A049330 5278968781483042969,37307713155613,9093099984535515162569,339781108897078469,168702835448329388944396777
%N A049330 Numerator of (1/Pi)*Integral_{x=0..oo} (sin(x)/x)^n dx.
%D A049330 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.4.3, p. 22.
%H A049330 T. D. Noe, <a href="/A049330/b049330.txt">Table of n, a(n) for n=1..100</a>
%H A049330 Ulrich Abel and Vitaliy Kushnirevych, <a href="https://doi.org/10.1007/s00591-023-00342-5">Sinc integrals revisited</a>, Mathematische Semesterberichte (2023).
%H A049330 Iskander Aliev, <a href="http://arxiv.org/abs/math/0503115">Siegel's Lemma and Sum-Distinct Sets</a>, (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]
%H A049330 Iskander Aliev and Martin Henk, <a href="https://arxiv.org/abs/2304.00120">Minkowski's successive minima in convex and discrete geometry</a>, arXiv:2304.00120 [math.MG], 2023.
%H A049330 Robert Baillie, David Borwein, and Jonathan M. Borwein, <a href="http://www.jstor.org/stable/27642636">Surprising Sinc Sums and Integrals</a>, Amer. Math. Monthly, 115 (2008), 888-901.
%H A049330 A. H. R. Grimsey, <a href="http://dx.doi.org/10.1080/14786444508521508">On the accumulation of chance effects and the Gaussian frequency distribution</a>, Phil. Mag., 36 (1945), 294-295.
%H A049330 R. G. Medhurst and J. H. Roberts, <a href="http://dx.doi.org/10.1090/S0025-5718-1965-0172446-8">Evaluation of the integral I_n(b) = (2/Pi)*Integral_{0..inf} (sin x / x)^n cos (bx) dx</a>, Math. Comp., 19 (1965), 113-117.
%H A049330 Jan W. H. Swanepoel, <a href="https://math.colgate.edu/~integers/z50/z50.pdf">A Short Simple Probabilistic Proof of a Well Known Identity and the Derivation of Related New Identities Involving the Bernoulli Numbers and the Euler Numbers</a>, Integers (2025) Vol. 25, Art. No. A50. See p. 1.
%H A049330 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SincFunction.html">Sinc Function</a>.
%F A049330 a(n) = numerator( n*A099765(n)/(2^n*(n-1)!) ). - _G. C. Greubel_, Apr 01 2022
%e A049330 1/2, 1/2, 3/8, 1/3, 115/384, 11/40, ...
%t A049330 Numerator[Table[Integrate[(Sin[x]/x)^n,{x,0,\[Infinity]}]/Pi,{n,25}]] (* _Harvey P. Dale_, Jan 01 2013 *)
%t A049330 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 *)
%o A049330 (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
%o A049330 (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
%Y A049330 Cf. Same as A002297 except for n=4 term, A049331.
%Y A049330 Cf. A002304, A002305.
%K A049330 nonn,frac,easy,nice
%O A049330 1,3
%A A049330 _N. J. A. Sloane_, Mark S. Riggs (msr1(AT)ra.msstate.edu), Dec 11 1999