OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..100
Wikipedia, Partition of a set
EXAMPLE
a(3) = 19 because the sum of the entries in the last blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 6+3+2+5+3 = 19.
MAPLE
a:= proc(h) option remember; local b; b:=
proc(n, m, s) option remember; `if`(n=0, s,
add(b(n-1, max(m, j), `if`(j<m, s, (h-n+1)+
`if`(j=m, s, 0))), j=1..m+1))
end: b(h, 0$2)
end:
seq(a(n), n=1..25);
MATHEMATICA
a[h_] := a[h] = Module[{b}, b[n_, m_, s_] := b[n, m, s] = If[n == 0, s, Sum[b[n-1, Max[m, j], If[j < m, s, h - n + 1 + If[j == m, s, 0]]], {j, 1, m + 1}]]; b[h, 0, 0]];
Array[a, 25] (* Jean-François Alcover, May 22 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 18 2017
STATUS
approved