OFFSET
0,2
COMMENTS
Is this the same sequence as A123854? - N. J. A. Sloane, Mar 21 2007
Almost certainly this is the same as A123854. - Michael Somos, Aug 23 2007
Asymptotic expansion of Gamma(N/2) / Gamma((N-1)/2) = (N/2)^(1/2) * (c(0) + c(1)/N + c(2)/N^2 + ... ). a(n) = denominator(c(n)). - Michael Somos, Aug 23 2007
REFERENCES
V. Romanovsky, On the Moments of the Standard Deviation and of the Correlation Coefficient in Samples from Normal, Metron 5(4) (1925), 3-46.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's Interesting Series, arXiv:1009.4274 [math-ph], 2010-2011. See the unnumbered table on p. 7.
F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's interesting series, Amer. Math. Monthly, 120 (2013), 116-130. See Table 4.
D. H. Lehmer, Interesting series involving the central binomial coefficient, Amer. Math. Monthly, 92(7) (1985), 449-457.
Eric Weisstein's World of Mathematics, Standard Deviation Distribution.
FORMULA
From G. C. Greubel, Jan 29 2020: (Start)
a(n) = denominator(Sum_{k=0..n} binomial(2*k, k)/8^k).
a(n) = denominator(binomial(1/4, n)). (End)
MAPLE
seq(denom(add(binomial(2*k, k)/8^k, k = 0 .. n)), n = 0..25); # G. C. Greubel, Jan 29 2020
MATHEMATICA
Table[Denominator[Sum[Binomial[2*k, k]/8^k, {k, 0, n}]], {n, 0, 25}] (* G. C. Greubel, Jan 29 2020 *)
PROG
(PARI) {a(n) = if( n<0, 0, 2^(3*n - subst( Pol( binary( n ) ), x, 1) ) ) } /* Michael Somos, Aug 23 2007 */
(Magma) [Denominator( &+[Binomial(2*k, k)/8^k: k in [0..n]] ): n in [0..25]]; // G. C. Greubel, Jan 29 2020
(Sage) [denominator( binomial(1/4, n) ) for n in (0..25)] # G. C. Greubel, Jan 29 2020
(GAP) List([0..25], n-> DenominatorRat(Sum([0..n], k-> Binomial(2*k, k)/8^k))); # G. C. Greubel, Jan 29 2020
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Oct 16 2003
STATUS
approved