OFFSET
0,3
COMMENTS
Number of ways to choose a factorization of each part of an integer partition of n. - Gus Wiseman, Sep 05 2018
This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1, g(n) = A001055(n). - Seiichi Manyama, Nov 14 2018
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
EXAMPLE
From Gus Wiseman, Sep 05 2018: (Start)
The a(6) = 14 partitions of 6 into sums of products:
6, 2*3,
5+1, 4+2, 2*2+2, 3+3,
4+1+1, 2*2+1+1, 3+2+1, 2+2+2,
3+1+1+1, 2+2+1+1,
2+1+1+1+1,
1+1+1+1+1+1.
(End)
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@Select[facs[n/d], Min@@#1>=d&], {d, Rest[Divisors[n]]}]];
Table[Length[Join@@Table[Tuples[facs/@ptn], {ptn, IntegerPartitions[n]}]], {n, 20}] (* Gus Wiseman, Sep 05 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Jan 20 2002
EXTENSIONS
Renamed by T. D. Noe, May 24 2011
STATUS
approved