Before trying the problem "note your opinion as to whether the observed pattern is known to continue, known not to continue, or not known at all."

Write down the positive integers. Take the first number. Delete the second after that, the third after that, and so on. Form the partial sums and repeat.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
2 6 11 18 26 35 46 58 71 85 101 118 136 155 175
6 24 50 96 154 225 326 444 580 735
24 120 274 600 1044 1624
120 720 1764
720

Does the pattern of factorials continue?