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A304939 Number of labeled nonempty hypertrees (connected antichains with no cycles) spanning some subset of {1,...,n} without singleton edges.

%I A304939 #13 Aug 27 2018 18:42:38
%S A304939 1,0,1,7,51,506,6843,118581,2504855,62370529,1788082153,57997339632,
%T A304939 2099638691439,83922479506503,3670657248913385,174387350448735877,
%U A304939 8942472292255441103,492294103555090048458,28958704109012732921523
%N A304939 Number of labeled nonempty hypertrees (connected antichains with no cycles) spanning some subset of {1,...,n} without singleton edges.
%H A304939 Andrew Howroyd, <a href="/A304939/b304939.txt">Table of n, a(n) for n = 0..200</a>
%F A304939 a(n) = A305004(n) - 1 for n > 0. - _Andrew Howroyd_, Aug 27 2018
%e A304939 The a(3) = 7 hypertrees are the following:
%e A304939   {{1,2}}
%e A304939   {{1,3}}
%e A304939   {{2,3}}
%e A304939   {{1,2,3}}
%e A304939   {{1,2},{1,3}}
%e A304939   {{1,2},{2,3}}
%e A304939   {{1,3},{2,3}}
%o A304939 (PARI) \\ here b(n) is A030019 with b(1)=0.
%o A304939 b(n)=if(n<2, n==0, sum(i=0, n, stirling(n-1, i, 2)*n^(i-1)));
%o A304939 a(n)=if(n<1, n==0, sum(k=1, n, binomial(n, k)*b(k))); \\ _Andrew Howroyd_, Aug 27 2018
%Y A304939 Cf. A030019, A035053, A048143, A134954, A134955, A134956, A134957, A134959, A144959, A303838, A304867, A304911, A304912, A304918, A305004.
%K A304939 nonn
%O A304939 0,4
%A A304939 _Gus Wiseman_, May 21 2018