cp's OEIS Frontend

For n>0, a(n) is the number of ways to partition [n] into blocks of size at most 3, order the blocks, order the elements within each block, and choose 2 elements from each block.

E.g.: a(6)=7200 since we have the following cases:

12,34,56: 720 such orderings, 1 way to choose two elements from each block;

123,456: 720 such orderings, 3*3 ways to choose two elements from each block;

so 720*1 + 720*9 = 7200 ways.