A304937 Number of unlabeled nonempty hypertrees with up to n vertices and no singleton edges.

1, 0, 1, 3, 7, 16, 38, 97, 262, 758, 2298, 7258, 23648, 79056, 269628, 935327, 3290259, 11714284, 42139052, 152963036, 559697096, 2062573999, 7649550571, 28534096987, 106994891145, 403119433265, 1525466082178, 5795853930651, 22102635416715, 84579153865569

Offset

0,4

Links

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

Formula

a(n) = a(n-1) + A035053(n) for n > 1, a(n) = 1 - n for n < 2.

Example

Non-isomorphic representatives of the a(5) = 16 hypertrees are the following:
{{1,2}}
{{1,2,3}}
{{1,2,3,4}}
{{1,2,3,4,5}}
{{1,3},{2,3}}
{{1,4},{2,3,4}}
{{1,5},{2,3,4,5}}
{{1,2,5},{3,4,5}}
{{1,2},{2,5},{3,4,5}}
{{1,3},{2,4},{3,4}}
{{1,4},{2,4},{3,4}}
{{1,4},{2,5},{3,4,5}}
{{1,5},{2,5},{3,4,5}}
{{1,3},{2,4},{3,5},{4,5}}
{{1,4},{2,5},{3,5},{4,5}}
{{1,5},{2,5},{3,5},{4,5}}

Prog

(PARI) \\ here b(n) is A007563 as vector
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
b(n)={my(v=[1]); for(i=2, n, v=concat([1], EulerT(EulerT(v)))); v}
seq(n)={my(u=b(n)); Vec(1 + (x*Ser(EulerT(u))*(1-x*Ser(u)) - x)/(1-x))} \\ Andrew Howroyd, Aug 27 2018

Crossrefs

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

Sequence in context: A364625 A196154 A227235 * A152090 A190528 A203611

Adjacent sequences: A304934 A304935 A304936 * A304938 A304939 A304940

Keyword

nonn

Author

Gus Wiseman, May 21 2018

Status

approved