A343094 Number of connected loopless labeled multigraphs with n edges.

1, 1, 4, 24, 201, 2199, 29879, 486231, 9228867, 200272157, 4892538679, 132901744486, 3974163191604, 129735825879843, 4591187990365503, 175081375829138149, 7157470516097359747, 312267811360305253384, 14481803617066951613463, 711413177916751077562759

Offset: 0

Author

Andrew Howroyd, Apr 14 2021

Keywords

• nonn

Links

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

Crossrefs

Row sums of A290776.

The unlabeled version is A050535.

Cf. A322152.

Programs

Mathematica

S[m_, n_] := Binomial[Binomial[m, 2] + n - 1, n];
R[nn_] := Module[{cc = Array[0&, {nn, nn}]}, cc[[1, 1]] = 1; For[m = 1, m <= nn, m++, For[n = 1, n <= nn - 1, n++, cc[[m, n + 1]] = S[m, n] - S[m - 1, n] - Sum[Sum[Binomial[m - 1, i - 1]*cc[[i, j + 1]]*S[m - i, n - j], {j, 1, n}], {i, 2, m - 1}]]]; cc // Transpose];
Total /@ R[20] (* Jean-François Alcover, Apr 15 2021, after Andrew Howroyd's code for A290776 *)

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, 2)))))}