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 A320222 Number of unlabeled rooted trees with n nodes in which the non-leaf branches directly under any given node are all equal. 12
 1, 1, 2, 4, 9, 18, 39, 78, 161, 324, 658, 1316, 2657, 5314, 10668, 21347, 42777, 85554, 171290, 342580, 685498, 1371037, 2742733, 5485466, 10972351, 21944711, 43892080, 87784323, 175574004, 351148008, 702307038, 1404614076, 2809249582, 5618499824, 11237042426 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This is a weaker condition than achirality (cf. A003238). LINKS Andrew Howroyd, Table of n, a(n) for n = 1..500 FORMULA a(n) = 1 + Sum_{k = 2...n-1} floor((n-1)/k) * a(k). a(n) ~ c * 2^n, where c = 0.3270422384018894564479397100499014525700668391191792769625407295138546463... - Vaclav Kotesovec, Sep 07 2019 EXAMPLE The a(1) = 1 through a(6) = 18 rooted 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(o)))                           ((((o))))  (o((oo)))                                      (o(o)(o))                                      (o(o(o)))                                      (oo((o)))                                      ((((oo))))                                      (((o)(o)))                                      (((o(o))))                                      ((o((o))))                                      (o(((o))))                                      (((((o))))) MATHEMATICA saue[n_]:=Sum[If[SameQ@@DeleteCases[ptn, 1], If[DeleteCases[ptn, 1]=={}, 1, saue[DeleteCases[ptn, 1][[1]]]], 0], {ptn, IntegerPartitions[n-1]}]; Table[saue[n], {n, 15}] PROG (PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + sum(k=2, n-1, (n-1)\k*v[k])); v} \\ Andrew Howroyd, Oct 26 2018 CROSSREFS Cf. A002541, A003238, A010766, A126656, A014668, A167865, A214577, A316782, A317099, A317100, A317712, A320230. Sequence in context: A327739 A018000 A329668 * A036610 A219755 A289846 Adjacent sequences:  A320219 A320220 A320221 * A320223 A320224 A320225 KEYWORD nonn AUTHOR Gus Wiseman, Oct 07 2018 STATUS approved

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Last modified March 30 15:42 EDT 2020. Contains 333127 sequences. (Running on oeis4.)