A324838 - OEIS

%I #5 Mar 19 2019 07:14:30

%S 1,0,1,2,5,10,28,64,169,422,1108,2872,7627,20202,54216,145867,395288

%N Number of unlabeled rooted trees with n nodes where the branches of no branch of the root form a submultiset of the branches of the root.

%e The a(1) = 1 through a(6) = 10 rooted trees:

%e   o  ((o))  ((oo))   ((ooo))    ((oooo))

%e             (((o)))  (((oo)))   (((ooo)))

%e                      ((o)(o))   ((o)(oo))

%e                      ((o(o)))   ((o(oo)))

%e                      ((((o))))  ((oo(o)))

%e                                 ((((oo))))

%e                                 (((o)(o)))

%e                                 (((o(o))))

%e                                 ((o((o))))

%e                                 (((((o)))))

%t submultQ[cap_,fat_]:=And@@Function[i,Count[fat,i]>=Count[cap,i]]/@Union[List@@cap];

%t rtall[n_]:=Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])];

%t Table[Length[Select[rtall[n],And@@Table[!submultQ[b,#],{b,#}]&]],{n,10}]

%Y Cf. A000081, A290689, A304360, A306844, A317787, A318185.

%Y Cf. A324694, A324696, A324704, A324738, A324744, A324758, A324759, A324765, A324768, A324771, A324839, A324840, A324844, A324846.

%K nonn,more

%O 1,4

%A _Gus Wiseman_, Mar 18 2019