OFFSET
0,5
COMMENTS
A strict tree of weight n > 0 is either a single node of weight n, or a sequence of two or more strict trees with strictly decreasing weights summing to n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
EXAMPLE
The a(7) = 6 strict trees: 15, (11 3 1), (9 5 1), (7 5 3), ((7 3 1) 3 1), ((5 3 1) 5 1).
MATHEMATICA
a[n_]:=a[n]=If[OddQ[n], 1, 0]+Sum[Times@@a/@ptn, {ptn, Select[IntegerPartitions[n], Length[#]>1&&OddQ[Length[#]]&&UnsameQ@@#&]}];
Table[a[n], {n, 1, 60, 2}]
PROG
(PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + polcoef(prod(k=1, n-1, 1 + v[k]*x^(2*k-1) + O(x^(2*n))) - prod(k=1, n-1, 1 - v[k]*x^(2*k-1) + O(x^(2*n))), 2*n-1)/2); v} \\ Andrew Howroyd, Aug 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 13 2018
EXTENSIONS
a(30)-a(37) from Alois P. Heinz, Mar 13 2018
STATUS
approved