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
Andrew Howroyd, Table of n, a(n) for n = 1..500
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 31 2020
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Feb 09 2020
STATUS
approved