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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• 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, 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.

Crossrefs

Cf. A002304, A002297, A002298.

Programs

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 *)

Extensions

More terms from Vaclav Kotesovec, Aug 10 2019