A322139 Number of labeled 2-connected simple graphs with n edges (the vertices are {1,2,...,k} for some k).

1, 1, 0, 1, 3, 18, 131, 1180, 12570, 154535, 2151439, 33431046, 573197723, 10743619285, 218447494812, 4787255999220, 112454930390211, 2818138438707516, 75031660452368001, 2114705500316025737, 62890323682634277951, 1967901134191778583146, 64623905086814216468839

Offset: 0

Author

Gus Wiseman, Nov 27 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100
• Gus Wiseman, The a(6) = 131 labeled 2-connected graphs with 6 edges.

Crossrefs

Cf. A002218, A013922, A123534, 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 + y + O(y*y^n))^binomial(k, 2) * x^k / k!) + O(x*x^n)))))))))} \\ Andrew Howroyd, Nov 29 2018

Formula

a(n) = Sum_{i=3..n} A123534(i, n). - Andrew Howroyd, Nov 30 2018

Extensions

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