OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400
Wikipedia, Partition of a set
FORMULA
a(n) = Sum_{k=0..n} A275281(n,k).
EXAMPLE
a(3) = 2: 123, 1|2|3.
a(4) = 7: 1234, 12|34, 13|24, 14|23, 1|23|4, 1|24|3, 1|2|3|4.
a(5) = 9: 12345, 12|3|45, 13|2|45, 1|234|5, 1|235|4, 14|2|35, 1|245|3, 15|2|34, 1|2|3|4|5.
MAPLE
b:= proc(n, s) option remember; `if`(n>s,
binomial(n-1, n-s-1), 1) +add(binomial(n-1, j-1)*
b(n-j, s+j) *binomial(s+j-1, j-1), j=1..(n-s)/2)
end:
a:= n-> b(n, 0):
seq(a(n), n=0..30);
MATHEMATICA
b[n_, s_] := b[n, s] = If[n > s, Binomial[n-1, n-s-1], 1] + Sum[Binomial[n - 1, j - 1]*b[n - j, s + j]*Binomial[s + j - 1, j - 1], {j, 1, (n-s)/2}];
a[n_] := b[n, 0];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 21 2016
STATUS
approved