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 A268085 #22 Sep 08 2022 08:46:15
%S A268085 0,1,8,75,784,8820,104544,1288287,16359200,212751396,2821056160,
%T A268085 38013731756,519227905728,7174705330000,100136810390400,
%U A268085 1409850293610375,20002637245262400,285732116760449700,4106497099278420000,59341164471850545900,861753537765219528000
%N A268085 a(n) = Catalan(n)^2*n.
%C A268085 The series whose terms are the quotients a(n)/A013709(n) is convergent to 1-3/Pi.(see formula).
%C A268085 Proof: Both the Wallis-Lambert-series-1=4/Pi-1 and the elliptic Euler-series=1-2/Pi are absolutely convergent series. Thus any linear combination of the terms of these series will be also absolutely convergent to the value of the linear combination of these series - in this case to 1-3/Pi. Q.E.D.
%C A268085 Apart from inclusion of a(0) the same as A145600. - _R. J. Mathar_, Feb 07 2016
%H A268085 Ralf Steiner, <a href="https://www.researchgate.net/publication/340005810_Beispiele_zur_modifizierten_Wallis-Lambert-Reihe">Beispiele zur modifizierten Wallis-Lambert-Reihe</a> (in German).
%F A268085 Sum_{n>=0} a(n)/A013709(n) = 1 - 3/Pi (see A089491).
%e A268085 For n=3 the a(3)= 75.
%t A268085 Table[CatalanNumber[n]^2 n, {n, 0, 20}]
%o A268085 (Magma) [Catalan(n)^2*n: n in [0..20]]; // _Vincenzo Librandi_, Jan 26 2016
%o A268085 (PARI) a(n) = n*(binomial(2*n, n)/(n+1))^2; \\ _Altug Alkan_, Jan 26 2016
%Y A268085 Cf. A000108, A013709.
%K A268085 nonn,easy
%O A268085 0,3
%A A268085 _Ralf Steiner_, Jan 26 2016
%E A268085 Corrected and extended by _Vincenzo Librandi_, Jan 26 2016