A304937 - OEIS

%I #14 Aug 27 2018 22:33:16

%S 1,0,1,3,7,16,38,97,262,758,2298,7258,23648,79056,269628,935327,

%T 3290259,11714284,42139052,152963036,559697096,2062573999,7649550571,

%U 28534096987,106994891145,403119433265,1525466082178,5795853930651,22102635416715,84579153865569

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

%H Andrew Howroyd, <a href="/A304937/b304937.txt">Table of n, a(n) for n = 0..200</a>

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

%e Non-isomorphic representatives of the a(5) = 16 hypertrees are the following:

%e {{1,2}}

%e {{1,2,3}}

%e {{1,2,3,4}}

%e {{1,2,3,4,5}}

%e {{1,3},{2,3}}

%e {{1,4},{2,3,4}}

%e {{1,5},{2,3,4,5}}

%e {{1,2,5},{3,4,5}}

%e {{1,2},{2,5},{3,4,5}}

%e {{1,3},{2,4},{3,4}}

%e {{1,4},{2,4},{3,4}}

%e {{1,4},{2,5},{3,4,5}}

%e {{1,5},{2,5},{3,4,5}}

%e {{1,3},{2,4},{3,5},{4,5}}

%e {{1,4},{2,5},{3,5},{4,5}}

%e {{1,5},{2,5},{3,5},{4,5}}

%o (PARI) \\ here b(n) is A007563 as vector

%o EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

%o b(n)={my(v=[1]); for(i=2, n, v=concat([1], EulerT(EulerT(v)))); v}

%o seq(n)={my(u=b(n)); Vec(1 + (x*Ser(EulerT(u))*(1-x*Ser(u)) - x)/(1-x))} \\ _Andrew Howroyd_, Aug 27 2018

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

%K nonn

%O 0,4

%A _Gus Wiseman_, May 21 2018