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A039647
Related to A000032 (Lucas numbers): (n-1)!*L(n).
4
1, 3, 8, 42, 264, 2160, 20880, 236880, 3064320, 44634240, 722131200, 12853209600, 249559833600, 5249378534400, 118911189196800, 2886037330176000, 74715282690048000, 2055161959538688000, 59855791774851072000, 1840125433884401664000, 59547709552131440640000
OFFSET
1,2
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.
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
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 *)
CROSSREFS
a(n) = A039692(n, 1) (first column of Fibonacci Jabotinsky-triangle).
Sequence in context: A038048 A051763 A074435 * A071533 A361716 A000240
KEYWORD
easy,nonn
STATUS
approved