A304968 Number of labeled hypertrees spanning some subset of {1,...,n}, with singleton edges allowed.

1, 2, 7, 48, 621, 12638, 351987, 12426060, 531225945, 26674100154, 1538781595999, 100292956964456, 7288903575373509, 584454485844541718, 51256293341752583499, 4880654469385955209092, 501471626403154217825457, 55300894427785157597436786

Offset: 0

Author

Gus Wiseman, May 22 2018

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A030019, A035053, A134954, A134955, A134956, A134957, A134958, A134959, A144959, A304386, A304867, A304911, A304912, A304918, A304968, A304970.

Programs

PARI

\\ here b(n) is A134958 with b(1)=1.
b(n)=if(n<2, n>=0, 2^n*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

Binomial transform of b(1) = 1, b(n) = A134958(n) otherwise.