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 A025752 #33 Aug 20 2025 08:58:26
%S A025752 1,1,21,637,22295,842751,33429123,1370594043,57564949806,
%T A025752 2462500630590,106872527367606,4692675519868518,208041948047504298,
%U A025752 9297874755046153626,418404363977076913170,18939770876029014936162,861759574859320179595371,39387481745040692914447251
%N A025752 7th-order Patalan numbers (generalization of Catalan numbers).
%H A025752 Vincenzo Librandi, <a href="/A025752/b025752.txt">Table of n, a(n) for n = 0..200</a>
%H A025752 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 A025752 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 A025752 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 A025752 G.f.: (8-(1-49*x)^(1/7))/7.
%F A025752 a(n) = 7^(n-1)*6*A034833(n-1)/n!, n >= 2, where 6*A034833(n-1)= (7*n-8)(!^7) = Product_{j=2..n} (7*j - 8). - _Wolfdieter Lang_
%F A025752 a(n) ~ 49^(n-1) / (Gamma(6/7) * n^(8/7)). - _Amiram Eldar_, Aug 20 2025
%t A025752 CoefficientList[Series[(8 - (1 - 49*x)^(1/7))/7, {x, 0, 20}], x] (* _Vincenzo Librandi_, Dec 29 2012 *)
%t A025752 a[n_] := 49^(n-1) * Pochhammer[6/7, n-1]/n!; a[0] = 1; Array[a, 20, 0] (* _Amiram Eldar_, Aug 20 2025 *)
%Y A025752 Cf. A034833, A220607.
%K A025752 nonn,easy
%O A025752 0,3
%A A025752 _Olivier Gérard_