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 A320221 Irregular triangle with zeros removed where T(n,k) is the number of unlabeled series-reduced rooted trees with n leaves in which every leaf is at height k. 1
 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 6, 1, 1, 7, 1, 1, 11, 4, 1, 13, 6, 1, 20, 16, 1, 23, 23, 1, 33, 46, 1, 40, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 LINKS EXAMPLE Triangle begins:   1   1   1   1  1   1  1   1  3   1  3   1  6  1   1  7  1   1 11  4   1 13  6   1 20 16   1 23 23   1 33 46   1 40 70 The T(11,3) = 6 rooted trees:    (((oo)(oo))((oo)(ooooo)))    (((oo)(oo))((ooo)(oooo)))    (((oo)(ooo))((oo)(oooo)))    (((oo)(ooo))((ooo)(ooo)))   (((oo)(oo))((oo)(oo)(ooo)))   (((oo)(ooo))((oo)(oo)(oo))) MATHEMATICA qurt[n_]:=If[n==1, {{}}, Join@@Table[Union[Sort/@Tuples[qurt/@ptn]], {ptn, Select[IntegerPartitions[n], Length[#]>1&]}]]; DeleteCases[Table[Length[Select[qurt[n], SameQ[##, k]&@@Length/@Position[#, {}]&]], {n, 10}, {k, 0, n-1}], 0, {2}] CROSSREFS Row sums are A120803. Second column is A083751. A regular version is A320179. Cf. A000669, A005804, A048816, A119262, A120803, A141268, A244925, A319312. Cf. A316624, A320154, A320155, A320160, A320172, A320173. Sequence in context: A146907 A322865 A238694 * A236939 A236936 A236915 Adjacent sequences:  A320218 A320219 A320220 * A320222 A320223 A320224 KEYWORD nonn,tabf,more AUTHOR Gus Wiseman, Oct 07 2018 STATUS approved

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Last modified May 30 17:45 EDT 2020. Contains 334728 sequences. (Running on oeis4.)