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 A320179 Regular triangle where T(n,k) is the number of unlabeled series-reduced rooted trees with n leaves in which every leaf is at height k. 8
 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 3, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 1, 6, 1, 0, 0, 0, 0, 0, 1, 7, 1, 0, 0, 0, 0, 0, 0, 1, 11, 4, 0, 0, 0, 0, 0, 0, 0, 1, 13, 6, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 23, 23, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,18 LINKS EXAMPLE Triangle begins:   1   0  1   0  1  0   0  1  1  0   0  1  1  0  0   0  1  3  0  0  0   0  1  3  0  0  0  0   0  1  6  1  0  0  0  0   0  1  7  1  0  0  0  0  0   0  1 11  4  0  0  0  0  0  0   0  1 13  6  0  0  0  0  0  0  0   0  1 20 16  0  0  0  0  0  0  0  0   0  1 23 23  0  0  0  0  0  0  0  0  0   0  1 33 46  0  0  0  0  0  0  0  0  0  0 The T(10,3) = 4 rooted trees:    (((oo)(oo))((oo)(oooo)))    (((oo)(oo))((ooo)(ooo)))    (((oo)(ooo))((oo)(ooo)))   (((oo)(oo))((oo)(oo)(oo))) MATHEMATICA qurt[n_]:=If[n==1, {{}}, Join@@Table[Union[Sort/@Tuples[qurt/@ptn]], {ptn, Select[IntegerPartitions[n], Length[#]>1&]}]]; Table[Length[Select[qurt[n], SameQ[##, k]&@@Length/@Position[#, {}]&]], {n, 14}, {k, 0, n-1}] CROSSREFS Row sums are A120803. Third column is A083751. An irregular version is A320221. Cf. A000669, A001678, A048816, A079500, A119262, A244925, A316655, A319312. Cf. A316624, A320154, A320155, A320160, A320172, A320173. Sequence in context: A111417 A007271 A327449 * A035656 A325675 A279948 Adjacent sequences:  A320176 A320177 A320178 * A320180 A320181 A320182 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Oct 07 2018 STATUS approved

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Last modified May 27 21:12 EDT 2020. Contains 334671 sequences. (Running on oeis4.)