A002304 - OEIS

A002304

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

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

Table of n, a(n) for n=0..15.

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

Cf. A002305, A002297, A002298.

Sequence in context: A196014 A266215 A192535 * A117516 A075726 A296776

Adjacent sequences: A002301 A002302 A002303 * A002305 A002306 A002307

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

More terms from Vaclav Kotesovec, Aug 10 2019

STATUS

approved