what's the explicit formula to the sequence 1/2 , 1 , 3 , 12 , 60 , 360 , 2520 , ...?

Question

what's the explicit formula to the sequence 1/2 , 1 , 3 , 12 , 60 , 360 , 2520 , ...?

 

Multiplies by one larger number each time but how to put that into an explicit formula?

Answer 1

The explicit formula (assuming the sequence begins with a₁) is:

     a_n = (1/2)(n!)

Answer 2

a_n = (a_n-1)(n), a₁ = 1/2

 

Check:

a₁ = 1/2

a₂ = (1/2)(2) = 1

a₃ = 1(3) = 3

a₄ = 3(4) = 12

a₅ = 12(5) = 60

a₆ = 60(6) = 360

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