My apologies, I was actually reacting generally to the fact that Excel
does not handle the results of a formula which resolves to "" very well
and not to this specific question.

Ragdyer wrote:
The OP asked that "no number" be present until a value was entered in
Column A.

What are your specs?
Can you accept a zero?

=IF(A1,SUM($A$1:A1),0)

Also, exactly what formula are you using, and in what way are you using
it, that's giving you an error?

There might be viable "workarounds".