

A300354


Number of enriched ptrees of weight n with distinct leaves.


7



1, 1, 1, 2, 2, 3, 8, 8, 13, 17, 54, 56, 98, 125, 195, 500, 606, 921, 1317, 1912, 2635, 6667, 7704, 12142, 16958, 24891, 33388, 47792, 106494, 126475, 195475, 268736, 393179, 523775, 750251, 979518, 2090669, 2457315, 3759380, 5066524, 7420874, 9726501, 13935546
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OFFSET

0,4


COMMENTS

An enriched ptree of weight n > 0 is either a single node of weight n, or a sequence of two or more enriched ptrees with weakly decreasing weights summing to n.


LINKS

Table of n, a(n) for n=0..42.


FORMULA

a(n) = Sum_{i=1..A000009(n)} A299203(A246867(n,i)).


EXAMPLE

The a(6) = 8 enriched ptrees with distinct leaves: 6, (42), (51), ((31)2), ((32)1), (3(21)), ((21)3), (321).


MATHEMATICA

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
ept[q_]:=ept[q]=If[Length[q]===1, 1, Total[Times@@@Map[ept, Join@@Function[sptn, Join@@@Tuples[Permutations/@GatherBy[sptn, Total]]]/@Select[sps[q], Length[#]>1&], {2}]]];
Table[Total[ept/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 1, 30}]


CROSSREFS

Cf. A000009, A000041, A063834, A196545, A246867, A273873, A281145, A289501, A290261, A294018, A296150, A299201, A299202, A299203, A300352, A300353, A300355.
Sequence in context: A153944 A046652 A319860 * A091681 A076541 A227380
Adjacent sequences: A300351 A300352 A300353 * A300355 A300356 A300357


KEYWORD

nonn


AUTHOR

Gus Wiseman, Mar 03 2018


STATUS

approved



