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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<<m), i, f)/f)))))); recurse(n, 0, #v, 0)}

seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n]=C(v[1..n-1], n-1)); v} \\ Andrew Howroyd, Feb 08 2020

CROSSREFS

Cf. A000081, A004111, A130091, A316793, A316794, A316795.

Sequence in context: A092684 A123915 A132832 * A079116 A109222 A191789

Adjacent sequences:  A316793 A316794 A316795 * A316797 A316798 A316799

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 14 2018

EXTENSIONS

Terms a(26) and beyond from Andrew Howroyd, Feb 08 2020

STATUS

approved

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