OFFSET
0,3
COMMENTS
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.
MATHEMATICA
With[{m = 20}, Range[0, m]! * CoefficientList[Series[1/(1 - x^2 - 3*x^3), {x, 0, m}], x]] (* Amiram Eldar, Oct 30 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Oct 30 2023
STATUS
approved