A322140 Number of labeled 2-connected multigraphs with n edges (the vertices are {1,2,...,k} for some k).

1, 1, 1, 2, 7, 37, 262, 2312, 24338, 296928, 4112957, 63692909, 1089526922, 20389411551, 414146189901, 9070116944468, 212983762029683, 5336570227705763, 142083405456873290, 4004953714929148655, 119128974685786590410, 3728639072095285867881

Offset: 0

Author

Gus Wiseman, Nov 27 2018

Keywords

• nonn

Comments

We consider a single edge to be 2-connected, so a(1) = 1.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100
• Gus Wiseman, The a(5) = 37 labeled 2-connected multigraphs with 5 edges.

Crossrefs

Cf. A002218, A002905, A013922, A275307, A291841, A304118, A304887, A322110, A322117, A322118, A322137, A322138.

Programs

PARI

seq(n)={Vec(1 + vecsum(Vec(serlaplace(log(x/serreverse(x*deriv(log(sum(k=0, n, 1/(1 - y + O(y*y^n))^binomial(k, 2) * x^k / k!) + O(x*x^n)))))))))} \\ Andrew Howroyd, Nov 29 2018

Extensions

Terms a(7) and beyond from Andrew Howroyd, Nov 29 2018