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

1,3

Links

Table of n, a(n) for n=1..18.

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

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

Sequence in context: A029808 A089915 A370939 * A337457 A346463 A346464

Adjacent sequences: A318694 A318695 A318696 * A318698 A318699 A318700

Keyword

nonn

Author

Gus Wiseman, Aug 31 2018

Status

approved