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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 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 April 10 22:34 EDT 2021. Contains 342858 sequences. (Running on oeis4.)