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

0,2

Links

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

Formula

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A277503 A317666 A316567 * A281263 A206153 A326338

Adjacent sequences: A304965 A304966 A304967 * A304969 A304970 A304971

Keyword

nonn

Author

Gus Wiseman, May 22 2018

Status

approved