OFFSET
1,2
COMMENTS
LINKS
James Burling, The Special Rational Sequence
FORMULA
a(n) = denominator((((n-1)!!)/(n!! * 2^((1 + (-1)^n)/2)))^((-1)^n)).
a(n) = denominator(g(1, n)) where g(m, n) = m if m = n; m/(2 * g(m + 1, n) otherwise.
EXAMPLE
For n = 1, a(1) = 1.
For n = 2, a(2) = 2 * 2 = 4.
For n = 6, a(6) = 2 * 2 * 4 * 2 = 32.
MAPLE
f:= n -> denom(((doublefactorial(n-1)) / (doublefactorial(n)*2^((1+(-1)^n)/2)))^((-1)^n)):
seq(f(n), n=1..100); # Robert Israel, Aug 06 2014
PROG
(PARI)
df(n) = prod(i=0, floor((n-1)/2), n-2*i) \\ Double factorial (n!!)
a(n) = denominator(((df(n-1)) / (df(n)*2^((1+(-1)^n)/2)))^((-1)^n))
vector(50, n, a(n)) \\ Colin Barker, Aug 06 2014
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
James Burling, Aug 06 2014
EXTENSIONS
More terms from Colin Barker, Aug 06 2014
STATUS
approved