HINT 19M: The product θ(θ + 1) ··· (θ + 11) = 39916800 θ + 120543840 θ² + 150917976 θ³ + 105258076 θ⁴ + 45995730 θ⁵ + 13339535 θ⁶ + 2637558 θ⁷ + 357423 θ⁸ + 32670 θ⁹ + 1925 θ¹⁰ + 66 θ¹¹ + θ¹².