A002305 Denominators of coefficients in asymptotic expansion of (2/Pi)*Integral_{0..oo} (sin x / x)^n dx. (Formerly M5106 N2211)

1, 20, 1120, 3200, 3942400, 66560000, 10035200000, 136478720000, 268461670400000, 56518246400000, 23658537943040000000, 51431604224000000, 70718455808000000, 102541760921600000, 23292891381760000000, 8879987916800000, 144993552704000000, 1072952290009600000

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..17.

David H. Bailey and Jonathan M. Borwein, Experimental computation with oscillatory integrals, Gems in experimental mathematics, 25-40, Contemp. Math., 517, Amer. Math. Soc., Providence, RI, 2010. [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; Denominator[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. A002304, A002297, A002298.

Sequence in context: A324416 A177596 A210835 * A091535 A265654 A152130

Adjacent sequences: A002302 A002303 A002304 * A002306 A002307 A002308

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Vaclav Kotesovec, Aug 10 2019

Status

approved