OFFSET
1,3
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.
FORMULA
a(n) = numerator((n/2^(n-1)) * sum((-1)^r*(n-2*r)^(n-1)/(r!*(n-r)!), r=0..n/2)). - Sean A. Irvine, Oct 01 2013
EXAMPLE
1, 1, 3/4, 2/3, 115/192, 11/20, ...
MATHEMATICA
a[n_] := Numerator[ (2/Pi)*Integrate[ (Sin[x]/x)^n, {x, 0, Infinity}] ]; Table[ a[n], {n, 1, 21}] (* Jean-François Alcover, Dec 19 2011 *)
Numerator@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 *)
PROG
(PARI) a(n) = numerator((n/2^(n-1)) * sum(r=0, n/2, (-1)^r*(n-2*r)^(n-1)/(r!*(n-r)!))); \\ Michel Marcus, Oct 02 2013
CROSSREFS
KEYWORD
nonn,frac,easy,nice
AUTHOR
EXTENSIONS
a(22)-a(23) from T. D. Noe, Feb 22 2014
STATUS
approved