A305004 Number of labeled hypertrees (connected acyclic antichains) spanning some subset of {1,...,n} without singleton edges.

1, 1, 2, 8, 52, 507, 6844, 118582, 2504856, 62370530, 1788082154, 57997339633, 2099638691440, 83922479506504, 3670657248913386, 174387350448735878, 8942472292255441104, 492294103555090048459, 28958704109012732921524

Offset: 0

Author

Gus Wiseman, May 23 2018

Keywords

• nonn

Examples

			The a(3) = 8 hypertrees:
{}
{{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, A134958, A134959, A304386, A304939, A304968, A304970.

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)=sum(k=0, n, binomial(n, k)*b(k)); \\ Andrew Howroyd, Aug 27 2018

Formula

a(n > 0) = A304939(n) + 1.

Binomial transform of A030019 if we assume A030019(1) = 0.