OFFSET
1,6
COMMENTS
An enriched p-tree of weight n > 0 is either a single node of weight n, or a finite sequence of two or more enriched p-trees with weakly decreasing weights summing to n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
EXAMPLE
Triangle begins:
1
1 1
1 1 2
1 2 4 5
1 2 6 11 12
1 3 10 26 38 34
1 3 13 39 87 117 92
1 4 19 69 181 339 406 277
...
The T(5,4) = 11 enriched p-trees: (((21)1)1), ((2(11))1), (((11)2)1), ((211)1), ((21)(11)), (((11)1)2), ((111)2), ((21)11), (2(11)1), ((11)21), (2111).
MATHEMATICA
eptrees[n_]:=Prepend[Join@@Table[Tuples[eptrees/@ptn], {ptn, Select[IntegerPartitions[n], Length[#]>1&]}], n];
Table[Length[Select[eptrees[n], Count[#, _Integer, {-1}]===k&]], {n, 8}, {k, n}]
PROG
(PARI) A(n)={my(v=vector(n)); for(n=1, n, v[n] = y + polcoef(1/prod(k=1, n-1, 1 - v[k]*x^k + O(x*x^n)), n)); apply(p->Vecrev(p/y), v)}
{ my(T=A(10)); for(n=1, #T, print(T[n])) } \\ Andrew Howroyd, Aug 26 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Mar 19 2018
STATUS
approved