# Problem 330: Euler's Number
An infinite sequence of real numbers a(n) is defined for all integers n
as follows: For example,a(0) = 11! + 12! + 13! + ... = e − 1 a(1) = e −
11! + 12! + 13! + ... = 2e − 3 a(2) = 2e − 31! + e − 12! + 13! + ... =
72 e − 6 with e = 2.7182818... being Euler's constant. It can be shown
that a(n) is of the form A(n) e + B(n)n! for integers A(n) and B(n). For
example a(10) = 328161643 e − 65269448610! . Find A(109) + B(109) and
give your answer mod 77 777 777.