|
|
A002304
|
|
Numerators of coefficients in asymptotic expansion of (2/Pi)*Integral_{0..inf} (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
|
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) page 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
|
|
|
|