OFFSET
0,4
COMMENTS
Also the number of ways to first choose a strict partition of 2n, then a subset of it summing to n.
FORMULA
a(n) = 2*A108796(n) for n > 1.
EXAMPLE
The a(0) = 1 through a(7) = 14 pairs:
()() . . (21)(3) (31)(4) (32)(5) (42)(6) (43)(7)
(3)(21) (4)(31) (41)(5) (51)(6) (52)(7)
(5)(32) (6)(42) (61)(7)
(5)(41) (6)(51) (7)(43)
(32)(41) (321)(6) (7)(52)
(41)(32) (42)(51) (7)(61)
(51)(42) (421)(7)
(6)(321) (43)(52)
(43)(61)
(52)(43)
(52)(61)
(61)(43)
(61)(52)
(7)(421)
MATHEMATICA
Table[Length[Select[Tuples[Select[IntegerPartitions[n], UnsameQ@@#&], 2], Intersection@@#=={}&]], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 19 2023
STATUS
approved