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A039647 Related to A000032 (Lucas numbers): (n-1)!*L(n). 4

%I #23 Oct 16 2023 01:36:25

%S 1,3,8,42,264,2160,20880,236880,3064320,44634240,722131200,

%T 12853209600,249559833600,5249378534400,118911189196800,

%U 2886037330176000,74715282690048000,2055161959538688000,59855791774851072000,1840125433884401664000,59547709552131440640000

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

%C Number of possible well-colored circuits.

%H C. Banderier, J.-M. Le Bars, and V. Ravelomanana, <a href="https://arxiv.org/abs/math/0411138">Generating functions for kernels of digraphs</a>, arXiv:math/0411138 [math.CO], 2004.

%F 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)).

%F a(n) = (n-1)*(a(n-1)+(n-2)*a(n-2)), for n > 2. - _Christian Krause_, Oct 15 2023

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

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

%Y Cf. A000032, A000142.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)