A290011 Number of ways to connect n nodes with n+1 edges to form a 2-edge-connected graph.

6, 85, 900, 9450, 104160, 1224720, 15422400, 207900000, 2993760000, 45924278400, 748280332800, 12913284384000, 235381386240000, 4520194398720000, 91233825306624000, 1931115968990208000, 42778526977105920000, 989887004576870400000, 23885015465274163200000

Offset

4,1

Links

Robert Israel, Table of n, a(n) for n = 4..448

Formula

a(n) = (n - 4)*(n!/8) + (n*(n - 1)/2 - 3)*(n!/12) = (n^2 + 2 n - 18)*(n!/24).

E.g.f.: x^4*(3*x^2+x-6)/(24*(x-1)^3). - Robert Israel, Jul 19 2017

Maple

seq((n^2 + 2 *n - 18)* n!/24, n=6..30); # Robert Israel, Jul 19 2017

Mathematica

Table[(n - 4) (n!/8) + (n (n - 1)/2 - 3) (n!/12), {n, 4, 22}] (* Michael De Vlieger, Jul 18 2017 *)

Prog

(PARI) a(n) = (n - 4)*(n!/8) + (n*(n - 1)/2 - 3)*(n!/12); \\ Michel Marcus, Jul 18 2017

Crossrefs

Cf. A001072, A052447, A054596, A095983

Sequence in context: A245232 A284522 A167252 * A164266 A136597 A381243

Adjacent sequences: A290008 A290009 A290010 * A290012 A290013 A290014

Keyword

easy,nonn

Author

Eugene Y. Q. Shen, Jul 17 2017

Status

approved