The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A304912 Number of non-isomorphic spanning hyperforests of weight n. 18
 1, 1, 2, 3, 6, 9, 18, 29, 56, 97, 186, 337, 657, 1238, 2442, 4768, 9569, 19174, 39151, 80154, 166211, 346239, 727853, 1537611, 3270710, 6989669, 15018389, 32405378, 70230238, 152772075, 333552711, 730632928, 1605459844, 3537861659, 7817447580, 17317397837 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A spanning hyperforest is an antichain of finite nonempty sets, which cover a set of n vertices, whose connected components are hypertrees (see A304867). The weight of a hypertree is the sum of cardinalities of its elements. Weight is generally not the same as number of vertices (see A134957). LINKS Andrew Howroyd, Table of n, a(n) for n = 0..500 FORMULA Euler transform of A304867. EXAMPLE The a(6) = 18 spanning hyperforests are the following:   {{1,2,3,4,5,6}}   {{1},{2,3,4,5,6}}   {{1,2},{3,4,5,6}}   {{1,5},{2,3,4,5}}   {{1,2,3},{4,5,6}}   {{1,2,5},{3,4,5}}   {{1},{2},{3,4,5,6}}   {{1},{2,3},{4,5,6}}   {{1},{2,5},{3,4,5}}   {{1,2},{3,4},{5,6}}   {{1,2},{3,5},{4,5}}   {{1,3},{2,4},{3,4}}   {{1,4},{2,4},{3,4}}   {{1},{2},{3},{4,5,6}}   {{1},{2},{3,4},{5,6}}   {{1},{2},{3,5},{4,5}}   {{1},{2},{3},{4},{5,6}}   {{1},{2},{3},{4},{5},{6}} PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} c(n)={my(v=[1]); for(i=2, ceil(n/2), v=concat([1], EulerT(concat([0], EulerT(v))))); v} seq(n)={my(u=c(n)); concat([1], EulerT(Vec(x*Ser(EulerT(u))*(1-x*Ser(u)) + (1 - x)*(Ser(u) - 1)+ O(x*x^n))))} \\ Andrew Howroyd, Aug 29 2018 CROSSREFS Cf. A007716, A035053, A048143, A054921, A134954, A134955, A134957, A144959, A286520, A293993, A293994, A304911, A304867. Sequence in context: A191398 A066313 A224958 * A018499 A107847 A059966 Adjacent sequences:  A304909 A304910 A304911 * A304913 A304914 A304915 KEYWORD nonn AUTHOR Gus Wiseman, May 20 2018 EXTENSIONS Terms a(10) and beyond from Andrew Howroyd, Aug 29 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)