OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..500
Wikipedia, Partition of a set
EXAMPLE
a(2) = 1: 1|2.
a(3) = 3: 12|3, 13|2, 1|23.
a(4) = 7: 123|4, 124|3, 12|34, 134|2, 13|2|4, 14|23, 1|234.
a(5) = 16: 1234|5, 1235|4, 123|45, 1245|3, 124|3|5, 125|34, 12|345, 1345|2, 134|2|5, 135|2|4, 13|25|4, 13|2|45, 145|23, 14|23|5, 15|234, 1|2345.
MAPLE
b:= proc(n, i, m, k) option remember; `if`(n=0, `if`(k=0, 1, 0),
add(`if`(j=i+1 and k=0, 0, b(n-1, j, max(m, j), k-
`if`(j=i+1, 1, 0))), j=1..m+1))
end:
a:= n-> b(n, 1, 0, 1):
seq(a(n), n=1..30);
MATHEMATICA
b[n_, i_, m_, k_] := b[n, i, m, k] = If[n == 0, If[k == 0, 1, 0], Sum[If[j == i + 1 && k == 0, 0, b[n - 1, j, Max[m, j], k - If[j == i + 1, 1, 0]]], {j, 1, m + 1}]];
a[n_] := b[n, 1, 0, 1];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 14 2016
STATUS
approved