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A366957
Expansion of e.g.f. 1/(1-x^2-3*x^3).
0
1, 0, 2, 18, 24, 720, 7200, 45360, 1128960, 14152320, 199584000, 4909766400, 82388275200, 1793381990400, 47163455539200, 1051370191872000, 29396519792640000, 863253387988992000, 24437860434763776000, 807966756915462144000, 27000346486744350720000
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