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A304937 Number of unlabeled nonempty hypertrees with up to n vertices and no singleton edges. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A211278 A196154 A227235 * A152090 A190528 A203611

Adjacent sequences:  A304934 A304935 A304936 * A304938 A304939 A304940

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 21 2018

STATUS

approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)