OFFSET
0,3
COMMENTS
Also the number of partitions of n in which each part occurs a factorial number of times.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Seiichi Manyama)
EXAMPLE
n | Partitions of n in which each part occurs a factorial number of times
--+----------------------------------------------------------------------
1 | 1;
2 | 2 = 1+1;
3 | 3 = 2+1;
4 | 4 = 3+1 = 2+2 = 2+1+1;
5 | 5 = 4+1 = 3+2 = 3+1+1 = 2+2+1;
6 | 6 = 5+1 = 4+2 = 4+1+1 = 3+2+1 = 3+3 = 2+2+1+1 = 1+1+1+1+1+1;
7 | 7 = 6+1 = 5+2 = 5+1+1 = 4+3 = 4+2+1 = 3+3+1 = 3+2+2 = 3+2+1+1;
MAPLE
b:= proc(n, i) option remember; local j; if n=0 then 1
elif i<1 then 0 else b(n, i-1); for j while
i*j!<=n do %+b(n-i*j!, i-1) od; % fi
end:
a:= n-> b(n$2):
seq(a(n), n=0..60); # Alois P. Heinz, May 11 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 11 2018
STATUS
approved