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 A316796 Number of unlabeled rooted trees with n nodes where the multiplicities in the multiset of branches under any given node are distinct. 5
 1, 1, 2, 3, 6, 11, 21, 40, 75, 139, 263, 498, 932, 1761, 3322, 6244, 11775, 22204, 41810, 78795, 148458, 279690, 527006, 993033, 1870881, 3525109, 6641904, 12514243, 23578708, 44426222, 83705148, 157713617, 297156310, 559886943, 1054911312, 1987613556 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 EXAMPLE The a(6) = 11 trees: (((((o))))) ((((oo)))) (((ooo))) (((o)(o))) ((oo(o))) ((oooo)) (oo((o))) (oo(oo)) (o(o)(o)) (ooo(o)) (ooooo) MATHEMATICA strut[n_]:=strut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1], UnsameQ@@Length/@Split[#]&]]; Table[Length[strut[n]], {n, 10}] PROG (PARI) C(v, n)={my(recurse(r, b, p, k)=if(!r, 1, sum(m=1, r, if(!bittest(b, m), sum(i=1, min(r\m, p), my(f=if(i==p, k+1, 1)); if(v[i]>=f, (v[i]-f+1)*self()(r-m*i, bitor(b, 1<

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)