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 A366173 #16 Jul 26 2025 20:28:10 %S A366173 1,1,1,2,1,8,4,1,24,42,8,1,64,276,184,16,1,162,1458,2298,732,32,1,400, %T A366173 6844,21232,16000,2752,64,1,976,29952,164680,240350,99756,9992,128,1, %U A366173 2368,125468,1142952,2882300,2320008,578420,35488,256 %N A366173 Triangle of coefficients of Caylerian polynomials. %H A366173 Giulio Cerbai and Anders Claesson, <a href="https://arxiv.org/abs/2310.01270">Caylerian polynomials</a>, arXiv:2310.01270 [math.CO], 2023. See p. 11. %H A366173 Giulio Cerbai and Anders Claesson, <a href="https://arxiv.org/abs/2411.08426">Enumerative aspects of Caylerian polynomials</a>, arXiv:2411.08426 [math.CO], 2024. See p. 2. %e A366173 Triangle begins: %e A366173 1 %e A366173 1 %e A366173 1 2 %e A366173 1 8 4 %e A366173 1 24 42 8 %e A366173 1 64 276 184 16 %e A366173 ... %e A366173 Because polynomials are: 1; 1; 1 + 2t; 1 + 8t + 4t^2; 1 + 24t + 42t^2 + 8t^3; 1 + 64t + 276t^2 + 184t^3 + 16t^4; ... %o A366173 (Python) %o A366173 from itertools import product %o A366173 def cayley_permutations(n): %o A366173 return [p for p in product(range(n), repeat=n) if len(set(p)) == max(p)+1] %o A366173 for n in range(1, 9): %o A366173 a = [0] * n %o A366173 for p in cayley_permutations(n): %o A366173 a[sum(x>y for x,y in zip(p, p[1:]))] += 1 %o A366173 print(a[::-1]) # _Andrei Zabolotskii_, Jul 26 2025 %Y A366173 Cf. A000670 (row sums), A365449 (alternating row sums). Column 1 seems to be twice A048776. %K A366173 nonn,tabf %O A366173 0,4 %A A366173 _Michel Marcus_, Oct 03 2023 %E A366173 Rows 6-9 from _Andrei Zabolotskii_, Jul 26 2025