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A002304 Numerators of coefficients in asymptotic expansion of (2/Pi)*Integral_{0..inf} (sin x / x)^n dx.
(Formerly M2939 N1182)
5

%I M2939 N1182

%S 1,-3,-13,27,52791,482427,-124996631,-5270328789,-7479063506161,

%T 6921977624613,10703530420192887741,-31023547697719285017327,

%U 4502691897987538544182239,-201974203900639732887399429,632827656013898657214770949567,-1732419272534268233524732551

%N Numerators of coefficients in asymptotic expansion of (2/Pi)*Integral_{0..inf} (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://www.carma.newcastle.edu.au/jon/oscillatory.pdf">Experimental computation with oscillatory integrals</a>, Comtemp. Math. 517 (2010) page 25 -40. [Added by _N. J. A. Sloane_, Nov 02 2009]

%H 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.

%t nmax = 20; Numerator[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. A002305, A002297, A002298.

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_.

%E Signs added by _N. J. A. Sloane_, Nov 02 2009

%E More terms from _Vaclav Kotesovec_, Aug 10 2019

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)