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

1,2

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

Links

Table of n, a(n) for n=1..35.

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

Cf. A163590 (numerators).

Sequence in context: A191452 A348685 A110485 * A154383 A022664 A316463

Adjacent sequences: A240985 A240986 A240987 * A240989 A240990 A240991

Keyword

frac,nonn

Author

James Burling, Aug 06 2014

Extensions

More terms from Colin Barker, Aug 06 2014

Status

approved