A002298 Denominator of (2/Pi)*Integral_{0..inf} (sin x / x)^n dx. (Formerly M3217 N1303)

1, 1, 4, 3, 192, 20, 11520, 315, 573440, 36288, 928972800, 1663200, 54499737600, 74131200, 1322526965760, 6810804000, 228532659683328000, 37638881280, 16783438527143608320, 121645100408832, 30370031620545576960000

Offset

1,3

Comments

Except for the n=4 term, equal to A049331/2.

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

T. D. Noe, Table of n, a(n) for n=1..100

A. H. R. Grimsey, On the accumulation of chance effects and the Gaussian frequency distribution, Phil. Mag., 36 (1945), 294-295.

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.

Example

1, 1, 3/4, 2/3, 115/192, 11/20, ...

Mathematica

Denominator[Table[2/Pi Integrate[(Sin[x]/x)^n, {x, 0, \[Infinity]}], {n, 25}]] (* Harvey P. Dale, Sep 04 2011 *)
Denominator@Table[Sum[(-1)^k (n-2k)^(n-1) Binomial[n, k], {k, 0, n/2}]/((n-1)! 2^(n-1)), {n, 1, 30}] (* Vladimir Reshetnikov, Sep 02 2016 *)

Crossrefs

Cf. A002297, A002304, A002305.

Sequence in context: A362674 A325871 A079324 * A195565 A368301 A356855

Adjacent sequences: A002295 A002296 A002297 * A002299 A002300 A002301

Keyword

nonn,frac,easy,nice

Author

N. J. A. Sloane

Extensions

Corrected and extended by Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 02 2001

Status

approved