1, 3, 9, 31, 128, 651, 3913

As per the details in the question the series is in the form of
Next term = ( Previous term × variable ) + ( 1 + variable )
First term = 1
Second term = First term × 1 + 2
⇒ Second term = 1 × 1 + 2 = 3 ;
Third term = Second term × 2 + 3
⇒ Third term = 3 × 2 + 3 = 9 ;
Similarly , we can find all others terms also.
Fourth term = Third term × 3 + 4
⇒ Fourth term = 9 × 3 + 4 = 31 ;
Fifth term = Fourth term × 4 + 5
⇒ Fifth term = 31 × 4 + 5 = 128 , is wrong . it should be 129 as fifth term .
Sixth term = Fifth term × 5 + 6
⇒ Sixth term = 129 × 5 + 6 = 651 ;
Seventh term = Sixth term × 6 + 7
⇒ Seventh term = 651 × 6 + 7 = 3913