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A301342 Regular triangle where T(n,k) is the number of rooted identity trees with n nodes and k leaves. 13
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, 1, 36 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Table of n, a(n) for n=1..93.

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

A version with the zeroes removed is A055327.

Cf. A000081, A001190, A003238, A004111, A032305, A055277, A273873, A276625, A277098, A290689, A298118, A298422, A298426, A301343, A301344, A301345.

Sequence in context: A123262 A191906 A187080 * A226369 A320751 A263764

Adjacent sequences:  A301339 A301340 A301341 * A301343 A301344 A301345

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Mar 19 2018

STATUS

approved

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)