OFFSET
1,3
COMMENTS
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.
The unique hyperforest (without loops) of order 1 is an isolated vertex, so a(1) = 1.
For n >= 2, a(n) - a(n-1) counts hyperforests of order n with components of order >= 3.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
EXAMPLE
a(3) = 3 since the only options are 2 hypertrees of order 3, or the forest composed by 3 isolated nodes.
PROG
(PARI) \\ here b(n) is A007563 as vector
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
b(n)={my(v=[1]); for(i=2, n, v=concat([1], EulerT(EulerT(v)))); v}
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Washington Bomfim, Sep 28 2008
STATUS
approved