OFFSET
1,12
EXAMPLE
Triangle begins:
1
1 0
1 0 0
1 1 0 0
1 2 0 0 0
1 4 1 0 0 0
1 6 5 0 0 0 0
1 9 13 2 0 0 0 0
1 12 28 11 0 0 0 0 0
1 16 53 40 3 0 0 0 0 0
1 20 91 109 26 0 0 0 0 0 0
1 25 146 254 116 6 0 0 0 0 0 0
1 30 223 524 387 61 0 0 0 0 0 0 0
The T(6,2) = 4 rooted identity trees: (((o(o)))), ((o((o)))), (o(((o)))), ((o)((o))).
MATHEMATICA
irut[n_]:=irut[n]=If[n===1, {{}}, Join@@Function[c, Select[Union[Sort/@Tuples[irut/@c]], UnsameQ@@#&]]/@IntegerPartitions[n-1]];
Table[Length[Select[irut[n], Count[#, {}, {-2}]===k&]], {n, 8}, {k, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Mar 19 2018
STATUS
approved