A039647 Related to A000032 (Lucas numbers): (n-1)!*L(n).

1, 3, 8, 42, 264, 2160, 20880, 236880, 3064320, 44634240, 722131200, 12853209600, 249559833600, 5249378534400, 118911189196800, 2886037330176000, 74715282690048000, 2055161959538688000, 59855791774851072000, 1840125433884401664000, 59547709552131440640000

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Number of possible well-colored circuits.

Links

• C. Banderier, J.-M. Le Bars, and V. Ravelomanana, Generating functions for kernels of digraphs, arXiv:math/0411138 [math.CO], 2004.

Crossrefs

a(n) = A039692(n, 1) (first column of Fibonacci Jabotinsky-triangle).

Cf. A000032, A000142.

Programs

Mathematica

nn=19;Drop[Range[0,nn]!CoefficientList[Series[Log[1/(1-x-x^2)],{x,0,nn}],x],1] (* Geoffrey Critzer, Jul 01 2013 *)

Formula

a(n) = (n-1)!*L(n), L(n) := A000032(n); E.g.f.: -log(1-x-x^2). Also a(n)/n! = sum(binomial(n-j, j)/(n-j), j=0..floor(n/2)).

a(n) = (n-1)*(a(n-1)+(n-2)*a(n-2)), for n > 2. - Christian Krause, Oct 15 2023