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 A204515 #30 Feb 03 2022 08:52:31
%S A204515 1,3,40,1050,42336,2328480,163088640,13913499600,1401656256000,
%T A204515 162984589447680,21497802046156800,3172717285311974400,
%U A204515 518147911684085760000,92790773980160256000000,18083066033253630689280000,3810158522787893903827200000
%N A204515 a(n) = (2*n)! * (2*n+1)! / ((n+1)^2 * n!^3).
%C A204515 Central terms of the triangle A247500.
%H A204515 Reinhard Zumkeller, <a href="/A204515/b204515.txt">Table of n, a(n) for n = 0..250</a>
%H A204515 G.-N. Han and H. Xiong, <a href="http://arxiv.org/abs/1508.00772">Difference operators for partitions and some applications</a>, arXiv preprint arXiv:1508.00772 [math.CO], 2015-2018.
%F A204515 a(n) = A248045(n+1) / (n+1).
%t A204515 Table[((2n)!(2n+1)!)/((n+1)^2 n!^3),{n,0,20}] (* _Harvey P. Dale_, May 17 2019 *)
%o A204515 (Haskell)
%o A204515 a204515 n = a247500 (2 * n) n
%o A204515 (PARI) a(n) = (2*n)! * (2*n+1)! / ((n+1)^2 * n!^3); \\ _Michel Marcus_, Feb 03 2022
%Y A204515 Cf. A000142, A247500, A248045.
%K A204515 nonn
%O A204515 0,2
%A A204515 _Reinhard Zumkeller_, Oct 19 2014