Help! Identifying the pattern in the given sequence

[TheShadow]

Hi everyone


I have this sequence here:


1 , 1 , 2 , 4 , 12 , 36 , 144 , 576 , 2880


I have to identify the pattern in that sequence, and find the next 3 terms. I found the next three terms, which are 14400, 86400 and 518400. You multiply the first 1 by 1 then the second 1 by 2 and then the 2 by two, then the next two numbers are gotten by multiplying by 3 and so on (x1 x2 x2 x3 x3 x4 x4 etc).


But how would I say that? How would I put "identifying the pattern" into words or an equation?


Thanks

 

[Ishuda]

I would describe it as a pair of statements (plus an initial statement). One statement for the even number indice and one statement for the odd number indicie. For example, look at the series as a pair of series; a_2n-1 and a_2n
a_2n-1 : 1, 2, 12, ...
a_2n : 1, 4, 36, ...
n = 1, 2, 3, ...
Well, looking at it this way
a₁ = 1
a_2n = n * a_2n-1; n = 1, 2, 3, ...
a_2n+1 = n * a_2n; n = 1, 2, 3,

EDIT: One could also introduce the greatest integer function, i.e.
[n] = m (an integer) so that n \(\displaystyle \le\) m \(\displaystyle \lt\) n+1,
that is the integer or int function, and write
a₁ = 1
a_n = [\(\displaystyle \frac{n+1}{2}\)] a_n-1

BTW: Check ALL of those equations out, I may have gotten off an index playing around