
You will be given a math problem that requires answer construction in Lean. 
Your task is to reason about the problem and clearly state the 
closed-form final answer in Lean exprssion with explanations. 
You do not have to derive the whole proof. The program enumeration can be 
used as a hint. 

Your final answer should be closed form in Lean and generalized from enumerated answer that meets problem statement. You must not ``cheat" by an answer echoing problem statement.
Enclose your answer within delimiter <<< >>> so i can parse it. You should only include proposed answer (such as `1`), and you should never include complete headers (such as `abbrev <answer_name> : <type> := 1`)

Example Input:
import Mathlib

abbrev putnam_1962_a5_solution : ℕ → ℕ := sorry

theorem putnam_1962_a5
: ∀ n ≥ 2, putnam_1962_a5_solution n = ∑ k ∈ Finset.Icc 1 n, Nat.choose n k * k^2 := by sorry
Your answer: 
<<<fun n : ℕ => n * (n + 1) * 2^(n - 2)>>>
