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

1,2

Links

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

Formula

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

Example

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

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

Crossrefs

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

Sequence in context: A034586 A268383 A092338 * A030601 A049839 A130233

Adjacent sequences: A199766 A199767 A199768 * A199770 A199771 A199772

Keyword

nonn

Author

Joshua Zucker, Nov 10 2011

Extensions

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

Status

approved