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A134959 Number of spanning hypertrees with n unlabeled vertices: analog of A035053 when edges of size 1 are allowed (with no two equal edges). 13
1, 2, 3, 10, 35, 150, 707, 3700, 20470, 119260, 719341, 4466316, 28367118, 183620874, 1207563011, 8049914664, 54295152117, 369981325578, 2544017965638, 17633790542978, 123108792874528, 865045359778662, 6114040341515978, 43443726772579152, 310195170229429300 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
Inverse Euler transform of A134957. - Gus Wiseman, May 20 2018
EXAMPLE
From Gus Wiseman, May 20 2018: (Start)
Non-isomorphic representatives of the a(3) = 10 hypertrees are the following:
{{1,2,3}}
{{3},{1,2,3}}
{{1,3},{2,3}}
{{2},{3},{1,2,3}}
{{2},{1,3},{2,3}}
{{3},{1,3},{2,3}}
{{1},{2},{3},{1,2,3}}
{{1},{2},{1,3},{2,3}}
{{2},{3},{1,3},{2,3}}
{{1},{2},{3},{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]}, 1 + x*ser[EulerT[u]]*(1 - x*ser[u]) + O[x]^n // CoefficientList[#, x]&];
seq[25] (* 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)); Vec(1 + x*Ser(EulerT(u))*(1-x*Ser(u)))} \\ Andrew Howroyd, Aug 27 2018
CROSSREFS
Sequence in context: A059735 A358213 A356926 * A270367 A056607 A278051
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 April 14 05:31 EDT 2024. Contains 371655 sequences. (Running on oeis4.)