A318697 Number of ways to partition a hypertree spanning n vertices into hypertrees.

1, 1, 7, 93, 1856, 49753, 1679441, 68463769, 3273695758, 179710285011, 11141016392749, 769939840667473, 58695964339179805, 4893452980658819151, 442915168219228586581, 43255083632741702266097, 4533695508041747494704359, 507638249638364368312476913

Offset: 1

Author

Gus Wiseman, Aug 31 2018

Keywords

• nonn

Examples

			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}}}
		

Crossrefs

Cf. A000272, A030019, A048143, A134954, A275307, A317631, A317632, A317634, A317635, A317677.

Programs

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}]