OFFSET
1,7
COMMENTS
Also the number of orderless Mathematica expressions with one atom, n positions, and no empty or unitary parts.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
EXAMPLE
The a(10) = 15 Mathematica expressions:
o[o,o[o,o[o,o]]]
o[o,o[o,o][o,o]]
o[o[o,o],o[o,o]]
o[o,o][o,o[o,o]]
o[o,o[o,o]][o,o]
o[o,o][o,o][o,o]
o[o,o[o,o,o,o,o]]
o[o,o,o[o,o,o,o]]
o[o,o,o,o[o,o,o]]
o[o,o,o,o,o[o,o]]
o[o,o][o,o,o,o,o]
o[o,o,o][o,o,o,o]
o[o,o,o,o][o,o,o]
o[o,o,o,o,o][o,o]
o[o,o,o,o,o,o,o,o]
MATHEMATICA
allOLZR[n_]:=allOLZR[n]=If[n==1, {"o"}, Join@@Cases[Table[PR[k, n-k-1], {k, n-1}], PR[h_, g_]:>Join@@Table[Apply@@@Tuples[{allOLZR[h], Select[Union[Sort/@Tuples[allOLZR/@p]], Length[#]>1&]}], {p, IntegerPartitions[g]}]]];
Table[Length[allOLZR[n]], {n, 25}]
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(v=[1]); for(n=2, n, my(t=EulerT(v)-v); v=concat(v, sum(k=1, n-2, v[k]*t[n-k-1]))); v} \\ Andrew Howroyd, Aug 19 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 15 2018
EXTENSIONS
Terms a(29) and beyond from Andrew Howroyd, Aug 19 2018
STATUS
approved