A304939 Number of labeled nonempty hypertrees (connected antichains with no cycles) spanning some subset of {1,...,n} without singleton edges.

1, 0, 1, 7, 51, 506, 6843, 118581, 2504855, 62370529, 1788082153, 57997339632, 2099638691439, 83922479506503, 3670657248913385, 174387350448735877, 8942472292255441103, 492294103555090048458, 28958704109012732921523

Offset

0,4

Links

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

Formula

a(n) = A305004(n) - 1 for n > 0. - Andrew Howroyd, Aug 27 2018

Example

The a(3) = 7 hypertrees are the following:
  {{1,2}}
  {{1,3}}
  {{2,3}}
  {{1,2,3}}
  {{1,2},{1,3}}
  {{1,2},{2,3}}
  {{1,3},{2,3}}

Prog

(PARI) \\ here b(n) is A030019 with b(1)=0.
b(n)=if(n<2, n==0, sum(i=0, n, stirling(n-1, i, 2)*n^(i-1)));
a(n)=if(n<1, n==0, sum(k=1, n, binomial(n, k)*b(k))); \\ Andrew Howroyd, Aug 27 2018

Crossrefs

Cf. A030019, A035053, A048143, A134954, A134955, A134956, A134957, A134959, A144959, A303838, A304867, A304911, A304912, A304918, A305004.

Sequence in context: A219306 A246572 A230883 * A352358 A293073 A368286

Adjacent sequences: A304936 A304937 A304938 * A304940 A304941 A304942

Keyword

nonn

Author

Gus Wiseman, May 21 2018

Status

approved