A240988 Denominators of the (reduced) rationals (((n-1)!!)/(n!! * 2^((1 + (-1)^n)/2)))^((-1)^n), where n is a positive integer.

1, 4, 2, 16, 8, 32, 16, 256, 128, 512, 256, 2048, 1024, 4096, 2048, 65536, 32768, 131072, 65536, 524288, 262144, 1048576, 524288, 8388608, 4194304, 16777216, 8388608, 67108864, 33554432, 134217728, 67108864, 4294967296, 2147483648, 8589934592, 4294967296

Offset: 1

Author

James Burling, Aug 06 2014

Keywords

• frac
• nonn

Comments

Numerators for this sequence are the swinging factorial A163590, starting from n = 1.

The terms are all powers of 2 (A000079).

It appears that a(2*n) = 2^A101925(n) and a(2*n+1) = 2^A005187(n). - Robert Israel, Aug 06 2014

Examples

			For n = 1, a(1) = 1.
For n = 2, a(2) = 2 * 2 = 4.
For n = 6, a(6) = 2 * 2 * 4 * 2 = 32.
		

Links

• James Burling, The Special Rational Sequence

Crossrefs

Cf. A163590 (numerators).

Programs

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

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

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.

Extensions

More terms from Colin Barker, Aug 06 2014