OFFSET
0,2
COMMENTS
An enriched r-tree of size n > 0 is either a single node of size n, or a finite sequence of enriched r-trees with weakly decreasing sizes summing to n - 1.
These are different from the R-trees of data science and the enriched R-trees of Bousquet-Mélou and Courtiel.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
FORMULA
O.g.f.: 1/(1 - x) + x Product_{i > 0} 1/(1 - a(i) x^i).
EXAMPLE
The a(3) = 8 enriched r-trees: 3, (2), ((1)), ((())), (11), (1()), (()1), (()()).
MATHEMATICA
ert[n_]:=ert[n]=1+Sum[Times@@ert/@y, {y, IntegerPartitions[n-1]}];
Array[ert, 30]
PROG
(PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + polcoef(1/prod(k=1, n-1, 1 - v[k]*x^k + O(x^n)), n-1)); concat([1], v)} \\ Andrew Howroyd, Aug 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 21 2018
STATUS
approved