A002304 Numerators of coefficients in asymptotic expansion of (2/Pi)*Integral_{0..oo} (sin x / x)^n dx.

1, -3, -13, 27, 52791, 482427, -124996631, -5270328789, -7479063506161, 6921977624613, 10703530420192887741, -31023547697719285017327, 4502691897987538544182239, -201974203900639732887399429, 632827656013898657214770949567, -1732419272534268233524732551

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• frac

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.

Crossrefs

Cf. A002305, A002297, A002298.

Programs

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 *)

Extensions

Signs added by N. J. A. Sloane, Nov 02 2009

More terms from Vaclav Kotesovec, Aug 10 2019