A134959 -id:A134959 - cp's OEIS frontend

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

Gus Wiseman, May 22 2018

nonn

			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}}

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

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

\\ 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

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

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

A304919 Number of labeled hyperforests spanning {1,...,n} and allowing singleton edges.

Original entry on oeis.org

1, 1, 5, 45, 665, 14153, 399421, 14137301, 603647601, 30231588689, 1738713049013, 112976375651901, 8186616300733321, 654642360222892057, 57267075701210437229, 5440407421313402397541, 557802495215406348358113, 61393838258161429159571873, 7220049654850517272144419941, 903546142463635579042416518989

Offset: 0

Gus Wiseman, May 21 2018

nonn

			The a(2) = 5 hyperforests are the following:
{{1,2}}
{{1},{2}}
{{1},{1,2}}
{{2},{1,2}}
{{1},{2},{1,2}}

Cf. A030019, A035053, A048143, A134954, A134955, A134956, A134957, A134959, A144959, A303838, A304717, A304867, A304911, A304912, A304918.

Inverse binomial transform of A134956.

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula