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A304970 Number of unlabeled hypertrees with up to n vertices and without singleton edges.

%I A304970 #17 Aug 28 2018 02:20:39
%S A304970 1,1,2,4,8,17,39,98,263,759,2299,7259,23649,79057,269629,935328,
%T A304970 3290260,11714285,42139053,152963037,559697097,2062574000,7649550572,
%U A304970 28534096988,106994891146,403119433266,1525466082179,5795853930652,22102635416716,84579153865570
%N A304970 Number of unlabeled hypertrees with up to n vertices and without singleton edges.
%H A304970 Andrew Howroyd, <a href="/A304970/b304970.txt">Table of n, a(n) for n = 0..200</a>
%F A304970 Partial sums of A035053 if we assume A035053(1) = 0.
%F A304970 a(n) = A304937(n) + 1 for n > 0.
%e A304970 Non-isomorphic representatives of the a(4) = 8 hypertrees are the following:
%e A304970 {}
%e A304970 {{1,2}}
%e A304970 {{1,2,3}}
%e A304970 {{1,2,3,4}}
%e A304970 {{1,3},{2,3}}
%e A304970 {{1,4},{2,3,4}}
%e A304970 {{1,3},{2,4},{3,4}}
%e A304970 {{1,4},{2,4},{3,4}}
%o A304970 (PARI) \\ here b(n) is A007563 as vector
%o A304970 EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
%o A304970 b(n)={my(v=[1]); for(i=2, n, v=concat([1], EulerT(EulerT(v)))); v}
%o A304970 seq(n)={my(u=b(n)); Vec(1 + (x*Ser(EulerT(u))*(1-x*Ser(u)))/(1-x))} \\ _Andrew Howroyd_, Aug 27 2018
%Y A304970 Cf. A030019, A035053, A134954, A134955, A134956, A134957, A134958, A134959, A144959, A304386, A304867, A304911, A304912, A304918, A304968, A304970.
%K A304970 nonn
%O A304970 0,3
%A A304970 _Gus Wiseman_, May 22 2018