A304977 Number of unlabeled hyperforests spanning n vertices with singleton edges allowed.

1, 1, 4, 14, 55, 235, 1112, 5672, 30783, 175733, 1042812, 6385278, 40093375, 257031667, 1676581863, 11098295287, 74401300872, 504290610004, 3451219615401, 23821766422463, 165684694539918, 1160267446543182, 8175446407807625, 57928670942338011, 412561582740147643

Offset

0,3

Links

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

Formula

Euler transform of b(1) = 1, b(n > 1) = A134959(n).

Example

Non-isomorphic representatives of the a(3) = 14 hyperforests are the following:
  {{1,2,3}}
  {{3},{1,2}}
  {{3},{1,2,3}}
  {{1,3},{2,3}}
  {{1},{2},{3}}
  {{2},{3},{1,3}}
  {{2},{3},{1,2,3}}
  {{3},{1,2},{2,3}}
  {{3},{1,3},{2,3}}
  {{1},{2},{3},{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}}

Prog

(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)); concat([1], EulerT(Vec(Ser(EulerT(u))*(1-x*Ser(u))-1)))} \\ Andrew Howroyd, Aug 27 2018

Crossrefs

Cf. A030019, A035053, A134954, A134955, A134956, A134957, A134958, A134959, A144959, A304867, A304911, A304912, A304918.

Sequence in context: A088655 A302288 A149490 * A143406 A329777 A323787

Adjacent sequences: A304974 A304975 A304976 * A304978 A304979 A304980

Keyword

nonn

Author

Gus Wiseman, May 22 2018

Extensions

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

Status

approved