A201883 The number of simple labeled graphs on n nodes such that i) all connected components have exactly one cycle, ii) all vertices have degree at most 3, iii) vertices of degree 3 are on a cycle.

1, 0, 0, 1, 15, 192, 2530, 36165, 570507, 9969400, 192525084, 4087525095, 94813475185, 2387594185944, 64886220442290, 1892895183489583, 58997625514583385, 1956486468000839280, 68781080882461076488, 2555098360335768584385, 100009432504671913008351

Offset

0,5

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: ((1-x)/(1-2x))^(1/2)*exp((x^2-2x)/(4(1-x)^2)).

a(n) ~ (2*n)^n/exp(n+3/4). - Vaclav Kotesovec, Sep 24 2013

From Benedict W. J. Irwin, May 25 2016: (Start)

Let y(0)=1, y(1)=0, y(2)=0, y(3)=1/6,

Let 4ny(n)-(14n+15)y(n+1)+(18n+36)y(n+2)-(10n+30)y(n+3)+(2n+8)y(n+4)=0,

a(n) = n!*y(n).

(End)

Mathematica

a = x/(1 - x); Range[0, 20]! CoefficientList[Series[Exp[Log[1/(1 - a)]/2 - a/2 - a^2/4], {x, 0, 20}], x]

Crossrefs

Sequence in context: A051545 A220528 A006238 * A324357 A172204 A015673

Adjacent sequences: A201880 A201881 A201882 * A201884 A201885 A201886

Keyword

nonn

Author

Geoffrey Critzer, Dec 06 2011

Status

approved