Let the initial terms of a sequence be {$1, 1, 1, 1, 2, 11, 84, 676, 5477, 44407$}.

Propagate this sequence backwards to produce $20$ new terms. Find the sum of these $20$ terms (written in simplest fraction form as $p/q$ ). What is the value of $(p*q) \mod (10^9+7)$?