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A331875
Number of enriched identity p-trees of weight n.
10
1, 1, 2, 3, 6, 14, 32, 79, 198, 522, 1368, 3716, 9992, 27612, 75692, 212045, 589478, 1668630, 4690792, 13387332, 37980664, 109098556, 311717768, 900846484, 2589449032, 7515759012, 21720369476, 63305262126, 183726039404, 537364221200, 1565570459800, 4592892152163
OFFSET
1,3
COMMENTS
An enriched identity p-tree of weight n is either the number n itself or a finite sequence of distinct enriched identity p-trees whose weights are weakly decreasing and sum to n.
LINKS
EXAMPLE
The a(1) = 1 through a(6) = 14 enriched p-trees:
1 2 3 4 5 6
(21) (31) (32) (42)
((21)1) (41) (51)
((21)2) (321)
((31)1) ((21)3)
(((21)1)1) ((31)2)
((32)1)
(3(21))
((41)1)
((21)21)
(((21)1)2)
(((21)2)1)
(((31)1)1)
((((21)1)1)1)
MATHEMATICA
eptrid[n_]:=Prepend[Select[Join@@Table[Tuples[eptrid/@p], {p, Rest[IntegerPartitions[n]]}], UnsameQ@@#&], n];
Table[Length[eptrid[n]], {n, 10}]
PROG
(PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + polcoef(prod(k=1, n-1, sum(j=0, n\k, j!*binomial(v[k], j)*x^(k*j)) + O(x*x^n)), n)); v} \\ Andrew Howroyd, Feb 09 2020
CROSSREFS
The orderless version is A300660.
The locally disjoint case is A331684.
Identity trees are A004111.
P-trees are A196545.
Enriched p-trees are A289501.
Sequence in context: A307231 A099968 A291401 * A010357 A190166 A238823
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 31 2020
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Feb 09 2020
STATUS
approved