cp's OEIS Frontend

A305004 Number of labeled hypertrees (connected acyclic antichains) spanning some subset of {1,...,n} without singleton edges.

%I A305004 #7 Aug 27 2018 18:43:02
%S A305004 1,1,2,8,52,507,6844,118582,2504856,62370530,1788082154,57997339633,
%T A305004 2099638691440,83922479506504,3670657248913386,174387350448735878,
%U A305004 8942472292255441104,492294103555090048459,28958704109012732921524
%N A305004 Number of labeled hypertrees (connected acyclic antichains) spanning some subset of {1,...,n} without singleton edges.
%H A305004 Andrew Howroyd, <a href="/A305004/b305004.txt">Table of n, a(n) for n = 0..200</a>
%F A305004 a(n > 0) = A304939(n) + 1.
%F A305004 Binomial transform of A030019 if we assume A030019(1) = 0.
%e A305004 The a(3) = 8 hypertrees:
%e A305004 {}
%e A305004 {{1,2}}
%e A305004 {{1,3}}
%e A305004 {{2,3}}
%e A305004 {{1,2,3}}
%e A305004 {{1,2},{1,3}}
%e A305004 {{1,2},{2,3}}
%e A305004 {{1,3},{2,3}}
%o A305004 (PARI) \\ here b(n) is A030019 with b(1)=0.
%o A305004 b(n)=if(n<2, n==0, sum(i=0, n, stirling(n-1, i, 2)*n^(i-1)));
%o A305004 a(n)=sum(k=0, n, binomial(n, k)*b(k)); \\ _Andrew Howroyd_, Aug 27 2018
%Y A305004 Cf. A030019, A035053, A134958, A134959, A304386, A304939, A304968, A304970.
%K A305004 nonn
%O A305004 0,3
%A A305004 _Gus Wiseman_, May 23 2018