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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

Table of n, a(n) for n=1..35.

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.)