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A316977 Number of series-reduced rooted trees whose leaves are {1, 1, 2, 2, 3, 3, ..., n, n}. 0
1, 12, 575, 66080, 13830706 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A rooted tree is series-reduced if every non-leaf node has at least two branches.

LINKS

Table of n, a(n) for n=1..5.

FORMULA

a(n) = A292505(A061742(n)). - Andrew Howroyd, Nov 19 2018

EXAMPLE

The a(2) = 12 trees are (1(1(22))), (1(2(12))), (1(122)), (2(1(12))), (2(2(11))), (2(112)), ((11)(22)), ((12)(12)), (11(22)), (12(12)), (22(11)), (1122).

MATHEMATICA

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];

gro[m_]:=If[Length[m]==1, m, Union[Sort/@Join@@(Tuples[gro/@#]&/@Select[mps[m], Length[#]>1&])]];

Table[Length[gro[Ceiling[Range[1/2, n, 1/2]]]], {n, 4}]

CROSSREFS

Cf. A000081, A000669, A007717, A020555, A050535, A094574, A292504, A316655, A316972, A316974.

Sequence in context: A192605 A192606 A179424 * A283490 A159722 A307948

Adjacent sequences:  A316974 A316975 A316976 * A316978 A316979 A316980

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 17 2018

STATUS

approved

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Last modified July 4 11:58 EDT 2020. Contains 335448 sequences. (Running on oeis4.)