OFFSET
0,3
COMMENTS
Take each Ferrers diagram of the partitions of n, label the cells within each row and then linearly order the rows.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..450
EXAMPLE
a(3) = 16 because the partitions of 3 can be so ordered in 16 ways: 3 (6); 2,1 (4); 1,1,1 (6).
MAPLE
b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j)*i!^j, j=0..n/i)))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..23); # Alois P. Heinz, Oct 02 2017
MATHEMATICA
p = Table[Map[Function[n, Apply[Times, n! ]], Partitions[i]], {i, 0, 20}]; q = Table[Map[Function[n, Length[n]! ], Partitions[i]], {i, 0, 20}]; Map[Function[n, Apply[Plus, n]], p*q]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, May 19 2009
STATUS
approved