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 A035097 #25 Aug 18 2025 02:12:38
%S A035097 1,45,2565,161595,10762227,742593663,52511980455,3780862592760,
%T A035097 276002969271480,20369019132235224,1516566060845513496,
%U A035097 113742454563413512200,8583180609746819651400,651095557682223033556200,49613481495385395156982440,3795431334396982729509156660
%N A035097 Related to 9-factorial numbers A045756.
%C A035097 Convolution of A035024(n-1) with A025754(n), n >= 1.
%H A035097 Michael De Vlieger, <a href="/A035097/b035097.txt">Table of n, a(n) for n = 1..526</a>
%H A035097 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 A035097 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A035097 a(n) = 9^(n-1)*A045756(n)/n!, where A045756(n) = (9*n-8)(!^9) = Product_{j=1..n} (9*j-8).
%F A035097 G.f.: (-1+(1-81*x)^(-1/9))/9.
%F A035097 D-finite with recurrence: n*a(n) + 9*(-9*n+8)*a(n-1) = 0. - _R. J. Mathar_, Jan 28 2020
%F A035097 a(n) ~ 9^(2*n-1) * n^(-8/9) / Gamma(1/9). - _Amiram Eldar_, Aug 18 2025
%t A035097 CoefficientList[Series[(1/(1-81 x)^(1/9)-1)/(9 x),{x,0,20}],x] (* _Harvey P. Dale_, May 14 2011 *)
%Y A035097 Cf. A045756, A035024, A025754, A034996, A256190.
%K A035097 easy,nonn
%O A035097 1,2
%A A035097 _Wolfdieter Lang_