A328055 Expansion of e.g.f. -log(1 - x / (1 - x)^2).
0, 1, 5, 32, 270, 2904, 38400, 605520, 11113200, 232888320, 5488560000, 143704108800, 4138573824000, 130020673305600, 4425201196416000, 162194862064435200, 6369479157000960000, 266808274486161408000, 11874724379464826880000, 559591797303082672128000
Offset: 0
Examples
For n=2, the 3 labeled octopuses are the following, and there are 2+2+1 ways to choose one element from each branch: O-1-2; O-2-1; 1-O-2. - _Enrique Navarrete_, Oct 29 2023
Crossrefs
Programs
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Magma
[0] cat [Factorial(n - 1)*(Lucas(2*n)-2):n in [1..20]]; // Marius A. Burtea, Oct 03 2019
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Mathematica
nmax = 19; CoefficientList[Series[-Log[1 - x/(1 - x)^2], {x, 0, nmax}], x] Range[0, nmax]! Join[{0}, Table[(n - 1)! (LucasL[2 n] - 2), {n, 1, 19}]] -
PARI
my(x='x+O('x^20)); concat(0, Vec(serlaplace(-log(1 - x / (1 - x)^2)))) \\ Michel Marcus, Oct 03 2019
Formula
E.g.f.: log(1 + Sum_{k>=1} Fibonacci(2*k) * x^k).
a(n) = (n - 1)! * (Lucas(2*n) - 2) for n > 0.
Comments