This is blowing my mind away ... this should be easy stuff!
Starting with the recursive formula $y_n=2n*y_{n-1}$ where $y_1=5.$ I'm trying to come up with a formula for the series { 5, 20, 120, 960, 9600, ... }. Just for fun, when I plug those values into the WolframAlpha sequence solver they present me with: $$a_n=5\cdot 2^{n-1}(1)_n$$ I have no idea what this $(1)_n$ term is about, but if I ignore it and evaluate the expression I get the series { 5, 10, 20, 40, 80, ... } - which is wrong! So I suspect this term I've ignored needs to be there ... but honestly guys ... I've never seen this notation ... ever ... could someone please clue me in? Thank you very much!
$a_n=5 \cdot 2^{n-1} n!$ works ... thanks!
... and thank you for the pointer to the Pochhammer symbol ... you learn something new every day! :-)
$\endgroup$ 11 Answer
$\begingroup$The $(1)_{n}$ term is the Pochammer symbol, defined by:
$$(a)_{n}\triangleq a(a+1)\cdots(a+n-1)$$
So in this case, the $n$th term could be determined by:
$$a_{n}=5 \times 2^{n-1} \times n!$$
$\endgroup$ 0
