A199769 Number of brackets in distinct sets with fewest possible elements.

1, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10

Offset: 1

Author

Joshua Zucker, Nov 10 2011

Keywords

• nonn

Examples

			There are three repetitions of 5 because of the sets {{{{{}}}}}, {{{}, {{}}}}, and {{{{}}}, {}}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..11306

Crossrefs

Differences of A198759. Also n repeated A004111(n) times.

Programs

Maple

b:= proc(n) a(n):= `if`(n<2, n, add(a(n-k)*add(b(d)*d*
     (-1)^(k/d+1), d=numtheory[divisors](k)), k=1..n-1)/(n-1))
    end:
T:= n-> n$b(n):
seq(T(n), n=1..10);  # Alois P. Heinz, May 05 2023

Formula

a(n) = A198759(n+1) - A198759(n).

Extensions

Second set in example corrected by Rick L. Shepherd, May 22 2013