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A304968 Number of labeled hypertrees spanning some subset of {1,...,n}, with singleton edges allowed.

%I A304968 #8 Aug 27 2018 18:43:21
%S A304968 1,2,7,48,621,12638,351987,12426060,531225945,26674100154,
%T A304968 1538781595999,100292956964456,7288903575373509,584454485844541718,
%U A304968 51256293341752583499,4880654469385955209092,501471626403154217825457,55300894427785157597436786
%N A304968 Number of labeled hypertrees spanning some subset of {1,...,n}, with singleton edges allowed.
%H A304968 Andrew Howroyd, <a href="/A304968/b304968.txt">Table of n, a(n) for n = 0..200</a>
%F A304968 Binomial transform of b(1) = 1, b(n) = A134958(n) otherwise.
%e A304968 The a(2) = 7 hypertrees are the following:
%e A304968 {}
%e A304968 {{1}}
%e A304968 {{2}}
%e A304968 {{1,2}}
%e A304968 {{1},{1,2}}
%e A304968 {{2},{1,2}}
%e A304968 {{1},{2},{1,2}}
%o A304968 (PARI) \\ here b(n) is A134958 with b(1)=1.
%o A304968 b(n)=if(n<2, n>=0, 2^n*sum(i=0, n, stirling(n-1, i, 2)*n^(i-1)));
%o A304968 a(n)=sum(k=0, n, binomial(n, k)*b(k)); \\ _Andrew Howroyd_, Aug 27 2018
%Y A304968 Cf. A030019, A035053, A134954, A134955, A134956, A134957, A134958, A134959, A144959, A304386, A304867, A304911, A304912, A304918, A304968, A304970.
%K A304968 nonn
%O A304968 0,2
%A A304968 _Gus Wiseman_, May 22 2018