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A199769
Number of brackets in distinct sets with fewest possible elements
1
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
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
KEYWORD
nonn
AUTHOR
Joshua Zucker, Nov 10 2011
EXTENSIONS
Second set in example corrected by Rick L. Shepherd, May 22 2013
STATUS
approved