OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..575
Wikipedia, Partition of a set
FORMULA
a(n) = A285362(n,1).
EXAMPLE
a(3) = 15 because the sum of the entries in the first blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 6+3+4+1+1 = 15.
MAPLE
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=1, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=1..30);
MATHEMATICA
a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[If[j == 1, # + {0, (h - n + 1)*#[[1]]}, #]&[b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, May 20 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 17 2017
STATUS
approved