Sum of First Elements

Author: mistertfy64

Define a function P(N) as a function takes an integer N as its input and returns a set of all permutations of every integer from 1 to N, inclusive.

For example:

• P(2) = {{1, 2}, {2, 1}} and
• P(3) = {{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}.

Define another function T(S) as a function takes a set as its input and returns the sum of the first element of each element in its set.

For example (referring to the example for P for the order of addends):

• T(P(2)) = 1 + 2, therefore, T(P(2)) = 3 and
• T(P(3)) = 1 + 1 + 2 + 2 + 3 + 3, therefore, T(P(3)) = 12.

The correct password is the remainder of T(P(5000)) divided by 1000000007.

Do not include digit separators (e.g., commas and/or dots) in your answer.

Correct Answers