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A002298 Denominator of (2/Pi)*Integral_{0..inf} (sin x / x)^n dx.
(Formerly M3217 N1303)
5
1, 1, 4, 3, 192, 20, 11520, 315, 573440, 36288, 928972800, 1663200, 54499737600, 74131200, 1322526965760, 6810804000, 228532659683328000, 37638881280, 16783438527143608320, 121645100408832, 30370031620545576960000 (list; graph; refs; listen; history; text; internal format)
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: A300026 A266255 A079324 * A195565 A197243 A175372

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

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Last modified June 16 19:43 EDT 2019. Contains 324155 sequences. (Running on oeis4.)