first digit = 1+2
second digit = digit from above operation that comes after + sign
third digit = multiply 1st and second digit
fourth digit = repeat first digit
fifth digit = add 1 to first or fourth digit
sixth digit = repeat whatever you did in previous step
seventh digit = you can get this digit by dividing 3rd digit by 2nd digit
That's one answer Paul's link came up with, although it expresses it as n^2 + n, rather than n * (n + 1). That's a pretty interesting site. I tried a bunch of sequences and it could nearly always derive the pattern.