A300354 Number of enriched p-trees of weight n with distinct leaves.

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

Offset

0,4

Comments

An enriched p-tree of weight n > 0 is either a single node of weight n, or a sequence of two or more enriched p-trees 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 p-trees 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