A304386 Number of unlabeled hypertrees (connected antichains with no cycles) spanning up to n vertices and allowing singleton edges.

1, 2, 5, 15, 50, 200, 907, 4607, 25077, 144337, 863678, 5329994, 33697112, 217317986, 1424880997, 9474795661, 63769947778, 433751273356, 2977769238994, 20611559781972, 143720352656500, 1008765712435162, 7122806053951140, 50566532826530292, 360761703055959592

Offset: 0

Author

Gus Wiseman, May 21 2018

Keywords

• nonn

Examples

			Non-isomorphic representatives of the a(3) = 15 hypertrees are the following:
  {}
  {{1}}
  {{1,2}}
  {{1,2,3}}
  {{2},{1,2}}
  {{1,3},{2,3}}
  {{3},{1,2,3}}
  {{1},{2},{1,2}}
  {{3},{1,2},{2,3}}
  {{3},{1,3},{2,3}}
  {{2},{3},{1,2,3}}
  {{1},{2},{3},{1,2,3}}
  {{2},{3},{1,2},{1,3}}
  {{2},{3},{1,3},{2,3}}
  {{1},{2},{3},{1,3},{2,3}}
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A030019, A035053, A048143, A054921, A134954, A134955, A134957, A134959, A144959, A304386, A304717, A304867, A304911, A304912, A304968, A304970.

Programs

PARI

\\ here b(n) is A318494 as vector
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
b(n)={my(v=[1]); for(i=2, n, v=concat([1], EulerT(EulerT(2*v)))); v}
seq(n)={my(u=2*b(n)); Vec(1 + x*Ser(EulerT(u))*(1-x*Ser(u))/(1-x))} \\ Andrew Howroyd, Aug 27 2018

Formula

Partial sums of b(1) = 1, b(n) = A134959(n) otherwise.

Extensions

Terms a(7) and beyond from Andrew Howroyd, Aug 27 2018