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Number of connected graphs with minimum degree at least 3 and with n vertices.
2

%I #11 Dec 25 2018 22:35:58

%S 1,26,1858,236926,53470032,21496173692,15580846842786,

%T 20666722709050752,50987383226899017116,237747620610010161018672,

%U 2125708489963555363039732518,36886187432874074894930307867796,1253964425811022692146824416678500176

%N Number of connected graphs with minimum degree at least 3 and with n vertices.

%C Generating function is K(x,1) in the reference, see page 405.

%D Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p.404-405.

%H Vaclav Kotesovec, <a href="/A257947/b257947.txt">Table of n, a(n) for n = 4..80</a>

%F a(n) ~ 2^(n*(n-1)/2).

%t Table[n!*SeriesCoefficient[Log[Sum[2^(k*(k-1)/2)*x^k*Exp[k*x*(x-1-k)/(2*(1+x))]/k!, {k, 0, n}]] - x*(2+x+x^2)/(4*(1+x)) - Log[1+x]/2, {x, 0, n}], {n, 4, 15}]

%Y Cf. A054853, A059166.

%K nonn

%O 4,2

%A _Vaclav Kotesovec_, May 14 2015