MathDB

Given is the set

M_n=\{0, 1, 2, \ldots, n\}

of nonnegative integers less than or equal to

n

. A subset

S

M_n

is called outstanding if it is non-empty and for every natural number

k\in S

, there exists a

k

-element subset

T_k

S

. Determine the number

a(n)

of outstanding subsets of

M_n

.
(41st Austrian Mathematical Olympiad, National Competition, part 1, Problem 3)

3