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

Author

Gus Wiseman, May 21 2018

Keywords

• nonn

Examples

			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}}
		

Links

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

Crossrefs

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

Programs

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

Formula

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