I want to find the generating function for a_{n}=n(n-1).

Am I justified in the second to last step, ignoring the summands for k=-1 and k=-2?

If so, is there a reason why I can ignore the first two terms?

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- May 29th 2013, 05:04 PMYuukiquestion on indices of a generating function
I want to find the generating function for a

_{n}=n(n-1).

Am I justified in the second to last step, ignoring the summands for k=-1 and k=-2?

If so, is there a reason why I can ignore the first two terms? - May 29th 2013, 05:05 PMProve ItRe: question on indices of a generating function
Is there such a thing as (-2)! or (-1)!?

- May 29th 2013, 05:08 PMYuukiRe: question on indices of a generating function
No, but I wasn't sure if (-2)! and (-1)! not existing allowed me to ignore them.

So because (-2)! and (-1)! don't exist, we can't evaluate them, hence it's okay to ignore them? - May 29th 2013, 05:10 PMProve ItRe: question on indices of a generating function
Only in this case, because you can see if you plug n=0 and n=1 into your original sum that those terms are 0 anyway.

Really what you should have written is

It doesn't make sense to put into your counter values which will give undefined terms. - May 29th 2013, 05:23 PMYuukiRe: question on indices of a generating function
Thank you very much, it now makes a lot of sense.