%I #10 Nov 30 2018 15:56:52

%S 1,1,0,1,3,18,131,1180,12570,154535,2151439,33431046,573197723,

%T 10743619285,218447494812,4787255999220,112454930390211,

%U 2818138438707516,75031660452368001,2114705500316025737,62890323682634277951,1967901134191778583146,64623905086814216468839

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

%H Andrew Howroyd, <a href="/A322139/b322139.txt">Table of n, a(n) for n = 0..100</a>

%H Gus Wiseman, <a href="/A322139/a322139.png">The a(6) = 131 labeled 2-connected graphs with 6 edges.</a>

%F a(n) = Sum_{i=3..n} A123534(i, n). - _Andrew Howroyd_, Nov 30 2018

%o (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

%Y Cf. A002218, A013922, A123534, A275307, A291841, A304118, A304887, A322110, A322117, A322118, A322137, A322138.

%K nonn

%O 0,5

%A _Gus Wiseman_, Nov 27 2018

%E Terms a(7) and beyond from _Andrew Howroyd_, Nov 29 2018