%I #9 Aug 28 2018 02:56:33
%S 1,1,3,7,16,41,108,301,881,2684,8455,27444,91248,309593,1068584,
%T 3742171,13269281,47561455,172092274,627887239,2307902495,8539497952,
%U 31786480760,118960956585,447413177185,1690336204778,6412656031161
%N a(n) = A134955(n) - A134955(n-2).
%C a(n) is the number of hyperforests with n unlabeled nodes without trees of order 2. This follows from the fact that for n >= 2 A134955(n-2) counts the hyperforests of order n with one or more trees of order 2.
%C The unique hyperforest (without loops) of order 1 is an isolated vertex, so a(1) = 1.
%C For n >= 2, a(n) - a(n-1) counts hyperforests of order n with components of order >= 3.
%H Andrew Howroyd, <a href="/A144977/b144977.txt">Table of n, a(n) for n = 1..200</a>
%e a(3) = 3 since the only options are 2 hypertrees of order 3, or the forest composed by 3 isolated nodes.
%o (PARI) \\ here b(n) is A007563 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(v)))); v}
%o seq(n)={my(u=b(n)); my(v=Vec(Ser(EulerT(u))*(1-x*Ser(u)))); EulerT(vector(#v, n, if(n<>2, v[n], 0)))} \\ _Andrew Howroyd_, Aug 27 2018
%Y Cf. A134955, A035053 (hypertrees).
%K nonn
%O 1,3
%A _Washington Bomfim_, Sep 28 2008