OFFSET
1,12
COMMENTS
A strict tree of weight n > 0 is either a single node of weight n, or a finite sequence of two or more strict trees with strictly decreasing weights summing to n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
EXAMPLE
Triangle begins:
1
1 0
1 1 0
1 1 1 0
1 2 2 1 0
1 2 4 4 1 0
1 3 7 9 7 1 0
1 3 10 19 20 11 1 0
1 4 15 35 51 43 16 1 0
The T(7,3) = 7 strict trees: ((51)1), ((42)1), ((41)2), ((32)2), (4(21)), ((31)3), (421).
MATHEMATICA
strtrees[n_]:=Prepend[Join@@Table[Tuples[strtrees/@ptn], {ptn, Select[IntegerPartitions[n], Length[#]>1&&UnsameQ@@#&]}], n];
Table[Length[Select[strtrees[n], Count[#, _Integer, {-1}]===k&]], {n, 12}, {k, n}]
PROG
(PARI) A(n)={my(v=vector(n)); for(n=1, n, v[n] = y + polcoef(prod(k=1, n-1, 1 + v[k]*x^k + O(x*x^n)), n)); vector(n, k, Vecrev(v[k]/y, k))}
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