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 A320172 Number of series-reduced balanced rooted identity trees whose leaves are integer partitions whose multiset union is an integer partition of n. 4
 1, 2, 5, 9, 19, 38, 79, 163, 352, 750, 1633, 3558, 7783, 17020, 37338, 81920, 180399, 398600, 885101, 1975638, 4435741, 10013855, 22726109, 51807432, 118545425, 272024659, 625488420, 1440067761, 3317675261, 7644488052, 17610215982, 40547552277, 93298838972, 214516498359, 492844378878 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A rooted tree is series-reduced if every non-leaf node has at least two branches, and balanced if all leaves are the same distance from the root. In an identity tree, all branches directly under any given node are different. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..500 EXAMPLE The a(1) = 1 through a(5) = 19 rooted identity trees:   (1)  (2)   (3)        (4)         (5)        (11)  (21)       (22)        (32)              (111)      (31)        (41)              ((1)(2))   (211)       (221)              ((1)(11))  (1111)      (311)                         ((1)(3))    (2111)                         ((1)(21))   (11111)                         ((2)(11))   ((1)(4))                         ((1)(111))  ((2)(3))                                     ((1)(31))                                     ((1)(22))                                     ((2)(21))                                     ((3)(11))                                     ((1)(211))                                     ((11)(21))                                     ((2)(111))                                     ((1)(1111))                                     ((11)(111))                                     ((1)(2)(11)) MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]]; gig[m_]:=Prepend[Join@@Table[Union[Sort/@Select[Sort/@Tuples[gig/@mtn], UnsameQ@@#&]], {mtn, Select[mps[m], Length[#]>1&]}], m]; Table[Sum[Length[Select[gig[y], SameQ@@Length/@Position[#, _Integer]&]], {y, Sort /@IntegerPartitions[n]}], {n, 8}] PROG (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)} seq(n)={my(u=vector(n, n, numbpart(n)), v=vector(n)); while(u, v+=u; u=WeighT(u)-u); v} \\ Andrew Howroyd, Oct 25 2018 CROSSREFS Cf. A000669, A005804, A048816, A079500, A119262, A120803, A141268, A292504, A300660, A319312. Cf. A320154, A320155, A320160, A320171, A320173, A320177, A320178, A320179. Sequence in context: A178841 A214319 A062092 * A079117 A030137 A243080 Adjacent sequences:  A320169 A320170 A320171 * A320173 A320174 A320175 KEYWORD nonn AUTHOR Gus Wiseman, Oct 07 2018 EXTENSIONS Terms a(13) and beyond from Andrew Howroyd, Oct 25 2018 STATUS approved

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Last modified September 18 21:51 EDT 2021. Contains 347536 sequences. (Running on oeis4.)