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

0,3

Links

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

Formula

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

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

Example

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}}

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

Crossrefs

Cf. A030019, A035053, A134958, A134959, A304386, A304939, A304968, A304970.

Sequence in context: A209307 A323843 A132228 * A151879 A191552 A154828

Adjacent sequences: A305001 A305002 A305003 * A305005 A305006 A305007

Keyword

nonn

Author

Gus Wiseman, May 23 2018

Status

approved