This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A328055 #17 Sep 05 2025 00:22:29
%S A328055 0,1,5,32,270,2904,38400,605520,11113200,232888320,5488560000,
%T A328055 143704108800,4138573824000,130020673305600,4425201196416000,
%U A328055 162194862064435200,6369479157000960000,266808274486161408000,11874724379464826880000,559591797303082672128000
%N A328055 Expansion of e.g.f. -log(1 - x / (1 - x)^2).
%C A328055 a(n) is the number of ways to choose one element from each branch of labeled octopuses with n nodes (cf. A029767 and example below). - _Enrique Navarrete_, Oct 29 2023
%F A328055 E.g.f.: log(1 + Sum_{k>=1} Fibonacci(2*k) * x^k).
%F A328055 a(n) = (n - 1)! * (Lucas(2*n) - 2) for n > 0.
%e A328055 For n=2, the 3 labeled octopuses are the following, and there are 2+2+1 ways to choose one element from each branch:
%e A328055 O-1-2;
%e A328055 O-2-1;
%e A328055 1-O-2. - _Enrique Navarrete_, Oct 29 2023
%t A328055 nmax = 19; CoefficientList[Series[-Log[1 - x/(1 - x)^2], {x, 0, nmax}], x] Range[0, nmax]!
%t A328055 Join[{0}, Table[(n - 1)! (LucasL[2 n] - 2), {n, 1, 19}]]
%o A328055 (Magma) [0] cat [Factorial(n - 1)*(Lucas(2*n)-2):n in [1..20]]; // _Marius A. Burtea_, Oct 03 2019
%o A328055 (PARI) my(x='x+O('x^20)); concat(0, Vec(serlaplace(-log(1 - x / (1 - x)^2)))) \\ _Michel Marcus_, Oct 03 2019
%Y A328055 Cf. A001906, A004146, A005248, A005443, A029767, A052567 (exponential transform), A100404, A226968, A328054.
%K A328055 nonn,changed
%O A328055 0,3
%A A328055 _Ilya Gutkovskiy_, Oct 03 2019