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The basic formula you might deploy is the one shown below. Enter the first number in A1, the formula in A2, and copy the formula down as far as you need. Then, if you delete a formula within the range the numbering will resume in the next cell with a formula.
[A2] =MAX(A$1:A1)+1
Key is the range definition, to wit A$1:A1. Note the $ sign. It makes the first row absolute. So, when copying down, A$1 will always remain just that while :A1 will change to :A2, :A3, :A4 etc. This range always starts with the row where you entered the starting number and ends with the row above the one where the formula resides. It's from this rule that the above formula got its funny appearance.
Of course, the next question is how to skip rows where you don't want a number. Consider a simple test.
[A2] =IF(NONTEXT(B2),MAX(A$1:A1)+1,"")
This formula will only insert a number if B2 has a numeric value, including a date. Consider its twin ISTEXT() and the cousins ISBLANK() and ISNUMBER().