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A002304 Numerators of coefficients in asymptotic expansion of (2/Pi)*Integral_{0..oo} (sin x / x)^n dx.
(Formerly M2939 N1182)
5
1, -3, -13, 27, 52791, 482427, -124996631, -5270328789, -7479063506161, 6921977624613, 10703530420192887741, -31023547697719285017327, 4502691897987538544182239, -201974203900639732887399429, 632827656013898657214770949567, -1732419272534268233524732551 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
David H. Bailey and Jonathan M. Borwein, Experimental computation with oscillatory integrals, Comtemp. Math. 517 (2010) pp. 25-40. [Added by N. J. A. Sloane, Nov 02 2009]
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.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A196014 A266215 A192535 * A117516 A075726 A296776
KEYWORD
sign,frac
AUTHOR
EXTENSIONS
Signs added by N. J. A. Sloane, Nov 02 2009
More terms from Vaclav Kotesovec, Aug 10 2019
STATUS
approved

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Last modified April 22 13:50 EDT 2024. Contains 371903 sequences. (Running on oeis4.)