%I M5106 N2211 #36 Apr 05 2024 11:10:14
%S 1,20,1120,3200,3942400,66560000,10035200000,136478720000,
%T 268461670400000,56518246400000,23658537943040000000,
%U 51431604224000000,70718455808000000,102541760921600000,23292891381760000000,8879987916800000,144993552704000000,1072952290009600000
%N Denominators of coefficients in asymptotic expansion of (2/Pi)*Integral_{0..oo} (sin x / x)^n dx.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H David H. Bailey and Jonathan M. Borwein, <a href="https://web.archive.org/web/20190313214007/https://carmamaths.org/resources/jon/oscillatory.pdf">Experimental computation with oscillatory integrals</a>, Gems in experimental mathematics, 25-40, Contemp. Math., 517, Amer. Math. Soc., Providence, RI, 2010. [Added by _N. J. A. Sloane_, Nov 02 2009]
%H R. G. Medhurst and J. H. Roberts, <a href="https://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.
%t nmax = 20; Denominator[CoefficientList[Simplify[Sum[3^k*(2*k)!/(k!*2^k*n^k) * SeriesCoefficient[Exp[n*(x^2/6 + Sum[(-1)^m*BernoulliB[2*m]* 2^(2*m - 1)*(x^(2*m)/(m*(2*m)!)), {m, 1, k}])], {x, 0, 2*k}], {k, 0, nmax}]], 1/n]] (* _Vaclav Kotesovec_, Aug 10 2019 *)
%Y Cf. A002304, A002297, A002298.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Vaclav Kotesovec_, Aug 10 2019