OFFSET
0,3
COMMENTS
A twice-partition of n is a sequence of integer partitions, one of each part of an integer partition of n.
FORMULA
G.f.: Product_{k>=2} 1/(1-A000041(k)*x^k).
EXAMPLE
The a(2) = 2 through a(5) = 13 twice-partitions:
(2) (3) (4) (5)
(11) (21) (22) (32)
(111) (31) (41)
(211) (221)
(1111) (311)
(2)(2) (2111)
(11)(2) (3)(2)
(2)(11) (11111)
(11)(11) (21)(2)
(3)(11)
(111)(2)
(21)(11)
(111)(11)
MATHEMATICA
twiptn[n_]:=Join@@Table[Tuples[IntegerPartitions/@ptn], {ptn, IntegerPartitions[n]}];
Table[Length[Select[twiptn[n], FreeQ[Total/@#, 1]&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 03 2022
STATUS
approved