(define (tree-count-min n) (cond
    [(<= n 1) n]
    [true (/ (/ (factorial (tree-count-min-helper n 1)) (factorial (+ (- n (tree-count-min-helper n 1)) 1))) (factorial (- (- (* 2 (tree-count-min-helper n 1)) n) 1)))]))

  (define (tree-count-min-helper n m) (if (<= m n) (tree-count-min-helper n (* m 2)) (/ m 2)))

  (define (factorial n) (cond
    [(<= n 1) n]
    [true (* n (factorial (- n 1)))]))