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%I #38 Aug 28 2018 00:26:29
%S 1,2,5,15,50,200,907,4607,25077,144337,863678,5329994,33697112,
%T 217317986,1424880997,9474795661,63769947778,433751273356,
%U 2977769238994,20611559781972,143720352656500,1008765712435162,7122806053951140,50566532826530292,360761703055959592
%N Number of unlabeled hypertrees (connected antichains with no cycles) spanning up to n vertices and allowing singleton edges.
%H Andrew Howroyd, <a href="/A304386/b304386.txt">Table of n, a(n) for n = 0..200</a>
%F Partial sums of b(1) = 1, b(n) = A134959(n) otherwise.
%e Non-isomorphic representatives of the a(3) = 15 hypertrees are the following:
%e {}
%e {{1}}
%e {{1,2}}
%e {{1,2,3}}
%e {{2},{1,2}}
%e {{1,3},{2,3}}
%e {{3},{1,2,3}}
%e {{1},{2},{1,2}}
%e {{3},{1,2},{2,3}}
%e {{3},{1,3},{2,3}}
%e {{2},{3},{1,2,3}}
%e {{1},{2},{3},{1,2,3}}
%e {{2},{3},{1,2},{1,3}}
%e {{2},{3},{1,3},{2,3}}
%e {{1},{2},{3},{1,3},{2,3}}
%o (PARI) \\ here b(n) is A318494 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(2*v)))); v}
%o seq(n)={my(u=2*b(n)); Vec(1 + x*Ser(EulerT(u))*(1-x*Ser(u))/(1-x))} \\ _Andrew Howroyd_, Aug 27 2018
%Y Cf. A030019, A035053, A048143, A054921, A134954, A134955, A134957, A134959, A144959, A304386, A304717, A304867, A304911, A304912, A304968, A304970.
%K nonn
%O 0,2
%A _Gus Wiseman_, May 21 2018
%E Terms a(7) and beyond from _Andrew Howroyd_, Aug 27 2018
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