OFFSET
0,6
FORMULA
a(n) = binomial(A000009(n),2).
EXAMPLE
The a(3) = 1 through a(8) = 15 pairs of strict partitions:
{3,21} {4,31} {5,32} {6,42} {7,43} {8,53}
{5,41} {6,51} {7,52} {8,62}
{41,32} {51,42} {7,61} {8,71}
{6,321} {52,43} {62,53}
{42,321} {61,43} {71,53}
{51,321} {61,52} {71,62}
{7,421} {8,431}
{43,421} {8,521}
{52,421} {53,431}
{61,421} {53,521}
{62,431}
{62,521}
{71,431}
{71,521}
{521,431}
MATHEMATICA
Table[Length[Subsets[Select[IntegerPartitions[n], UnsameQ@@#&], {2}]], {n, 0, 30}]
CROSSREFS
For non-strict partitions we have A355389.
The ordered version is 2*a(n).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 08 2023
STATUS
approved