## Sunday, 17 February 2013

### SUNDAY, 17 FEBRUARY 2013

Today is $48^{th}$ day of the year.

$48$ is the double factorial of $6$, written $6!!$

The value of the double factorial of a number $n$ is defined as follows:
If $n = -1$ or $n = 0$ then $n!! = 1$ otherwise $n!! = n.(n - 2)!!$

Given $n = 6$ then $6!! = 6.4!! = 6.4.2!! = 6.4.2.0!! = 6.4.2.1 = 48$
However, if $n = 5$ then $5!! = 5.3!! = 5.3.1!! = 5.3.1 = 15$
Thus, $6!!.5!! = 6.4.2.1.5.3.1 = 6.5.4.3.2.1 = 6!$
or, equivalently:
$$n!!.(n - 1)!! = n!$$