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A306200 Number of unlabeled rooted semi-identity trees with n nodes. 19
0, 1, 1, 2, 4, 8, 18, 41, 98, 237, 591, 1488, 3805, 9820, 25593, 67184, 177604, 472177, 1261998, 3388434, 9136019, 24724904, 67141940, 182892368, 499608724, 1368340326, 3756651116, 10336434585, 28499309291, 78727891420, 217870037932, 603934911859, 1676720329410 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A rooted tree is a semi-identity tree if the non-leaf branches of the root are all distinct and are themselves semi-identity trees.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2166

EXAMPLE

The a(1) = 1 through a(7) = 8 trees:

  o  (o)  (oo)   (ooo)    (oooo)     (ooooo)

          ((o))  ((oo))   ((ooo))    ((oooo))

                 (o(o))   (o(oo))    (o(ooo))

                 (((o)))  (oo(o))    (oo(oo))

                          (((oo)))   (ooo(o))

                          ((o(o)))   (((ooo)))

                          (o((o)))   ((o)(oo))

                          ((((o))))  ((o(oo)))

                                     ((oo(o)))

                                     (o((oo)))

                                     (o(o(o)))

                                     (oo((o)))

                                     ((((oo))))

                                     (((o(o))))

                                     ((o)((o)))

                                     ((o((o))))

                                     (o(((o))))

                                     (((((o)))))

MAPLE

b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,

      add(b(n-i*j, i-1)*binomial(a(i), j), j=0..n/i))

    end:

a:= n-> `if`(n=0, 0, b(n-1$2)):

seq(a(n), n=0..35);  # Alois P. Heinz, Jan 29 2019

MATHEMATICA

ursit[n_]:=Join@@Table[Select[Union[Sort/@Tuples[ursit/@ptn]], UnsameQ@@DeleteCases[#, {}]&], {ptn, IntegerPartitions[n-1]}];

Table[Length[ursit[n]], {n, 10}]

CROSSREFS

Cf. A000081, A004111, A276625, A301700, A306201, A316471, A316474, A317708, A317712, A317718.

Sequence in context: A274547 A112483 A151381 * A057151 A026699 A182780

Adjacent sequences:  A306197 A306198 A306199 * A306201 A306202 A306203

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 29 2019

EXTENSIONS

More terms from Alois P. Heinz, Jan 29 2019

STATUS

approved

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Last modified February 26 14:18 EST 2021. Contains 341632 sequences. (Running on oeis4.)