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 A025753 #32 Aug 20 2025 08:58:31
%S A025753 1,1,28,1120,51520,2555392,132880384,7137574912,392566620160,
%T A025753 21983730728960,1248675905404928,71742106565083136,
%U A025753 4161042180774821888,243260927491451125760,14317643160925409116160,847604475126784219676672,50432466270043661070761984,3014081513550844685170245632
%N A025753 8th-order Patalan numbers (generalization of Catalan numbers).
%H A025753 Vincenzo Librandi, <a href="/A025753/b025753.txt">Table of n, a(n) for n = 0..200</a>
%H A025753 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 A025753 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 A025753 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 A025753 G.f.: (9-(1-64*x)^(1/9))/8.
%F A025753 a(n) = 8^(n-1)*7*A034975(n-1)/n!, n >= 2, where 7*A034975(n-1)= (8*n-9)!^8 = Product_{j=2..n} (8*j - 9). - _Wolfdieter Lang_
%F A025753 a(n) ~ 64^(n-1) / (Gamma(7/8) * n^(9/8)). - _Amiram Eldar_, Aug 20 2025
%t A025753 CoefficientList[Series[(9 - (1 - 64*x)^(1/8))/8, {x, 0, 20}], x] (* _Vincenzo Librandi_, Dec 29 2012 *)
%t A025753 a[n_] := 64^(n-1) * Pochhammer[7/8, n-1]/n!; a[0] = 1; Array[a, 20, 0] (* _Amiram Eldar_, Aug 20 2025 *)
%Y A025753 Cf. A034975, A203146.
%K A025753 nonn,easy
%O A025753 0,3
%A A025753 _Olivier Gérard_