A257947 Number of connected graphs with minimum degree at least 3 and with n vertices.

1, 26, 1858, 236926, 53470032, 21496173692, 15580846842786, 20666722709050752, 50987383226899017116, 237747620610010161018672, 2125708489963555363039732518, 36886187432874074894930307867796, 1253964425811022692146824416678500176

Offset: 4

Author

Vaclav Kotesovec, May 14 2015

Keywords

• nonn

Comments

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

References

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 4..80

Crossrefs

Cf. A054853, A059166.

Programs

Mathematica

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}]

Formula

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