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 A317712 Number of uniform rooted trees with n nodes. 21
 1, 1, 2, 4, 8, 15, 35, 72, 169, 388, 934, 2234, 5508, 13557, 33883, 85017, 215091, 546496, 1396524, 3582383, 9228470, 23852918, 61857180, 160871716, 419516462, 1096671326, 2873403980, 7544428973, 19847520789, 52308750878, 138095728065, 365153263313, 966978876376 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS An unlabeled rooted tree is uniform if the multiplicities of the branches directly under any given node are all equal. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..2250 (terms 1..200 from Andrew Howroyd) Gus Wiseman, All 72 uniform rooted trees with 8 nodes. FORMULA a(n) ~ c * d^n / n^(3/2), where d = 2.774067238136373782458114960391469140405537808253... and c = 0.43338208953061974806801546569720246018271214... - Vaclav Kotesovec, Sep 07 2019 EXAMPLE The a(5) = 8 uniform rooted trees:   ((((o))))   (((oo)))   ((o(o)))   ((ooo))   (o((o)))   (o(oo))   ((o)(o))   (oooo) MATHEMATICA purt[n_]:=Join@@Table[Select[Union[Sort/@Tuples[purt/@ptn]], SameQ@@Length/@Split[#]&], {ptn, IntegerPartitions[n-1]}]; Table[Length[purt[n]], {n, 10}] PROG (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)} seq(n)={my(v=[1]); for(n=2, n, my(t=WeighT(v)); v=concat(v, sumdiv(n-1, d, t[d]))); v} \\ Andrew Howroyd, Aug 28 2018 CROSSREFS Cf. A000081, A001190, A004111, A072774, A301700, A317588. Cf. A317705, A317707, A317708, A317709, A317710, A317711, A317717, A317718. Sequence in context: A036661 A145671 A316522 * A108693 A026096 A098864 Adjacent sequences:  A317709 A317710 A317711 * A317713 A317714 A317715 KEYWORD nonn AUTHOR Gus Wiseman, Aug 05 2018 EXTENSIONS Term a(21) and beyond from Andrew Howroyd, Aug 28 2018 STATUS approved

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Last modified August 5 21:45 EDT 2021. Contains 346488 sequences. (Running on oeis4.)