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 A025754 #35 Aug 20 2025 08:58:34
%S A025754 1,1,36,1836,107406,6766578,446594148,30432201228,2122646035653,
%T A025754 150707868531363,10850966534258136,790147653994615176,
%U A025754 58075852568604215436,4302080463351219958836,320812285981333831216056,24060921448600037341204200,1813591954188227814593266575
%N A025754 9th-order Patalan numbers (generalization of Catalan numbers).
%H A025754 Vincenzo Librandi, <a href="/A025754/b025754.txt">Table of n, a(n) for n = 0..200</a>
%H A025754 Wolfdieter Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LANG/lang.html">On generalizations of Stirling number triangles</a>, J. Integer Seq., Vol. 3 (2000), Article 00.2.4.
%H A025754 Elżbieta Liszewska and Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%H A025754 Thomas M. Richardson, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Richardson/rich2.html">The Super Patalan Numbers</a>, J. Int. Seq. 18 (2015), Article 15.3.3; <a href="http://arxiv.org/abs/1410.5880">arXiv preprint</a>, arXiv:1410.5880 [math.CO], 2014.
%F A025754 G.f.: (10-(1-81*x)^(1/9))/9.
%F A025754 a(n) = 9^(n-1)*8*A035022(n-1)/n!, n >= 2, where 8*A035022(n-1)= (9*n-10)(!^9)= Product_{j=2..n} (9*j - 10). - _Wolfdieter Lang_
%F A025754 Conjecture: n*a(n) + 9*(-9*n+10)*a(n-1) = 0. - _R. J. Mathar_, Jul 28 2014
%F A025754 a(n) ~ 81^(n-1) / (Gamma(8/9) * n^(10/9)). - _Amiram Eldar_, Aug 20 2025
%t A025754 CoefficientList[Series[(10-(1-81x)^(1/9))/9,{x,0,20}],x] (* _Harvey P. Dale_, Nov 29 2012 *)
%t A025754 a[n_] := 81^(n-1) * Pochhammer[8/9, n-1]/n!; a[0] = 1; Array[a, 20, 0] (* _Amiram Eldar_, Aug 20 2025 *)
%Y A025754 Cf. A035022.
%K A025754 nonn
%O A025754 0,3
%A A025754 _Olivier Gérard_