OFFSET
1,3
EXAMPLE
The a(3) = 7 hypertree partitions:
{{{1,2,3}}}
{{{1,2},{1,3}}}
{{{1,2},{2,3}}}
{{{1,3},{2,3}}}
{{{1,2}},{{1,3}}}
{{{1,2}},{{2,3}}}
{{{1,3}},{{2,3}}}
MATHEMATICA
trct[n_]:=Sum[StirlingS2[n-1, i]*n^(i-1), {i, 0, n-1}];
numSetPtnsOfType[ptn_]:=Total[ptn]!/Times@@Factorial/@ptn/Times@@Factorial/@Length/@Split[ptn];
Table[Sum[n^(Length[ptn]-1)*Product[trct[s+1], {s, ptn}]*numSetPtnsOfType[ptn], {ptn, IntegerPartitions[n-1]}], {n, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 31 2018
STATUS
approved