OFFSET
0,4
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>=1} 1/(1-(A000041(k)-1)*x^k).
EXAMPLE
The a(2) = 1 through a(6) = 19 twice-partitions:
(11) (21) (22) (32) (33)
(111) (31) (41) (42)
(211) (221) (51)
(1111) (311) (222)
(11)(11) (2111) (321)
(11111) (411)
(21)(11) (2211)
(111)(11) (3111)
(21111)
(111111)
(21)(21)
(22)(11)
(31)(11)
(111)(21)
(21)(111)
(211)(11)
(111)(111)
(1111)(11)
(11)(11)(11)
MATHEMATICA
twiptn[n_]:=Join@@Table[Tuples[IntegerPartitions/@ptn], {ptn, IntegerPartitions[n]}];
Table[Length[Select[twiptn[n], FreeQ[Length/@#, 1]&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 03 2022
STATUS
approved