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 A134957 Number of hyperforests with n unlabeled vertices: analog of A134955 when edges of size 1 are allowed (with no two equal edges). 19
 1, 2, 6, 20, 75, 310, 1422, 7094, 37877, 213610, 1256422, 7641700, 47735075, 304766742, 1981348605, 13079643892, 87480944764, 591771554768, 4042991170169, 27864757592632, 193549452132550, 1353816898675732, 9529263306483357, 67457934248821368, 480019516988969011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 FORMULA Euler transform of A134959. - Gus Wiseman, May 20 2018 EXAMPLE From Gus Wiseman, May 20 2018: (Start) Non-isomorphic representatives of the a(3) = 20 hyperforests are the following:   {}   {{1}}   {{1,2}}   {{1,2,3}}   {{1},{2}}   {{1},{2,3}}   {{2},{1,2}}   {{3},{1,2,3}}   {{1,3},{2,3}}   {{1},{2},{3}}   {{1},{2},{1,2}}   {{1},{3},{2,3}}   {{2},{3},{1,2,3}}   {{2},{1,3},{2,3}}   {{3},{1,3},{2,3}}   {{1,2},{1,3},{2,3}}   {{1},{2},{3},{2,3}}   {{1},{2},{3},{1,2,3}}   {{1},{2},{1,3},{2,3}}   {{2},{3},{1,3},{2,3}}   {{3},{1,2},{1,3},{2,3}}   {{1},{2},{3},{1,3},{2,3}}   {{2},{3},{1,2},{1,3},{2,3}}   {{1},{2},{3},{1,2},{1,3},{2,3}} (End) MATHEMATICA etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b]; EulerT[v_List] := With[{q = etr[v[[#]]&]}, q /@ Range[Length[v]]]; ser[v_] := Sum[v[[i]] x^(i - 1), {i, 1, Length[v]}] + O[x]^Length[v]; b[n_] := Module[{v = {1}}, For[i = 2, i <= n, i++, v = Join[{1}, EulerT[EulerT[2 v]]]]; v]; seq[n_] := Module[{u = 2 b[n]}, Join[{1}, EulerT[ser[EulerT[u]]*(1 - x*ser[u]) + O[x]^n // CoefficientList[#, x]&]]]; seq[24] (* Jean-François Alcover, Feb 10 2020, after Andrew Howroyd *) PROG (PARI) \\ here b(n) is A318494 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(2*v)))); v} seq(n)={my(u=2*b(n)); concat([1], EulerT(Vec(Ser(EulerT(u))*(1-x*Ser(u)))))} \\ Andrew Howroyd, Aug 27 2018 CROSSREFS Cf. A030019, A035053, A048143, A054921, A134955, A134957, A134959, A144959, A304867, A304911. Sequence in context: A150167 A150168 A145870 * A052889 A263901 A150169 Adjacent sequences:  A134954 A134955 A134956 * A134958 A134959 A134960 KEYWORD nonn AUTHOR Don Knuth, Jan 26 2008 EXTENSIONS Terms a(7) and beyond from Andrew Howroyd, Aug 27 2018 STATUS approved

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)