A322152 Number of labeled connected multigraphs with loops with n edges (the vertices are {1,2,...,k} for some k).

1, 2, 7, 39, 314, 3359, 45000, 725269, 13670256, 295099184, 7179749707, 194399095705, 5797793490859, 188855813757729, 6671188010874785, 254007814638737649, 10370334196814589256, 451923738493729293016, 20937747226064522726151, 1027666505638118490940059

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Mathematica

multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
Table[Length[Select[multsubs[multsubs[Range[n+1], 2], n], And[Union@@#==Range[Max@@Union@@#], Length[csm[#]]==1]&]], {n, 5}]

Prog

(PARI)
Connected(v)={my(u=vector(#v)); for(n=1, #u, u[n]=v[n] - sum(k=1, n-1, binomial(n-1, k)*v[k]*u[n-k])); u}
seq(n)={Vec(vecsum(Connected(vector(2*n, j, 1/(1 - x + O(x*x^n))^binomial(j+1, 2)))))} \\ Andrew Howroyd, Nov 28 2018

Crossrefs

Row sums of A322148. The unlabeled version is A007719.

Cf. A000272, A000664, A007718, A191646, A191970, A322114, A322115, A322147, A322151.

Sequence in context: A125660 A112944 A060073 * A368927 A336185 A187806

Adjacent sequences: A322149 A322150 A322151 * A322153 A322154 A322155

Keyword

nonn

Author

Gus Wiseman, Nov 28 2018

Extensions

Terms a(7) and beyond from Andrew Howroyd, Nov 28 2018

Status

approved