OFFSET
1,3
COMMENTS
An odd enriched p-tree of weight n > 0 is either a single node of weight n, or a finite odd-length sequence of at least 3 odd enriched 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(6) = 7 odd enriched p-trees: 6, (411), (321), (222), ((111)21), ((211)11), (21111).
MATHEMATICA
f[n_]:=f[n]=1+Sum[Times@@f/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&OddQ[Length[#]]&]}];
Array[f, 40]
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*x^n)) - 1/prod(k=1, n-1, 1 + v[k]*x^k + O(x*x^n)), n)/2); v} \\ Andrew Howroyd, Aug 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 05 2018
STATUS
approved